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Journal articles on the topic 'Optimization (Mathematical Theory)'

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Published: 4 June 2021

Last updated: 31 July 2024

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1

Lewis, Adrian S., and Michael L. Overton. "Eigenvalue optimization." Acta Numerica 5 (January 1996): 149–90. http://dx.doi.org/10.1017/s0962492900002646.

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Optimization problems involving eigenvalues arise in many different mathematical disciplines. This article is divided into two parts. Part I gives a historical account of the development of the field. We discuss various applications that have been especially influential, from structural analysis to combinatorial optimization, and we survey algorithmic developments, including the recent advance of interior-point methods for a specific problem class: semidefinite programming. In Part II we primarily address optimization of convex functions of eigenvalues of symmetric matrices subject to linear constraints. We derive a fairly complete mathematical theory, some of it classical and some of it new. Using the elegant language of conjugate duality theory, we highlight the parallels between the analysis of invariant matrix norms and weakly invariant convex matrix functions. We then restrict our attention further to linear and semidefinite programming, emphasizing the parallel duality theory and comparing primal-dual interior-point methods for the two problem classes. The final section presents some apparently new variational results about eigenvalues of nonsymmetric matrices, unifying known characterizations of the spectral abscissa (related to Lyapunov theory) and the spectral radius (as an infimum of matrix norms).

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Johri, Pravin K. "Derivation of duality in mathematical programming and optimization theory." European Journal of Operational Research 73, no. 3 (March 1994): 547–54. http://dx.doi.org/10.1016/0377-2217(94)90251-8.

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3

Dinesh, T. B., Magne Haveraaen, and Jan Heering. "An Algebraic Programming Style for Numerical Software and Its Optimization." Scientific Programming 8, no. 4 (2000): 247–59. http://dx.doi.org/10.1155/2000/494281.

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The abstract mathematical theory of partial differential equations (PDEs) is formulated in terms of manifolds, scalar fields, tensors, and the like, but these algebraic structures are hardly recognizable in actual PDE solvers. The general aim of the Sophus programming style is to bridge the gap between theory and practice in the domain of PDE solvers. Its main ingredients are a library of abstract datatypes corresponding to the algebraic structures used in the mathematical theory and an algebraic expression style similar to the expression style used in the mathematical theory. Because of its emphasis on abstract datatypes, Sophus is most naturally combined with object-oriented languages or other languages supporting abstract datatypes. The resulting source code patterns are beyond the scope of current compiler optimizations, but are sufficiently specific for a dedicated source-to-source optimizer. The limited, domain-specific, character of Sophus is the key to success here. This kind of optimization has been tested on computationally intensive Sophus style code with promising results. The general approach may be useful for other styles and in other application domains as well.

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Chiang, Mung, Steven H. Low, A. Robert Calderbank, and John C. Doyle. "Layering as Optimization Decomposition: A Mathematical Theory of Network Architectures." Proceedings of the IEEE 95, no. 1 (January 2007): 255–312. http://dx.doi.org/10.1109/jproc.2006.887322.

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Xidonas, Panos, Christis Hassapis, George Mavrotas, Christos Staikouras, and Constantin Zopounidis. "Multiobjective portfolio optimization: bridging mathematical theory with asset management practice." Annals of Operations Research 267, no. 1-2 (October 11, 2016): 585–606. http://dx.doi.org/10.1007/s10479-016-2346-6.

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6

LIN, JING-YUE, and ZI-HOU YANG. "Mathematical Control Theory of Singular Systems." IMA Journal of Mathematical Control and Information 6, no. 2 (1989): 189–98. http://dx.doi.org/10.1093/imamci/6.2.189.

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Manea, Daniela-Ioana, Emilia Țiţan, Radu R. Șerban, and Mihaela Mihai. "Statistical applications of optimization methods and mathematical programming." Proceedings of the International Conference on Applied Statistics 1, no. 1 (October 1, 2019): 312–28. http://dx.doi.org/10.2478/icas-2019-0028.

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Abstract Optimization techniques perform an important role in different domains of statistic. Examples of parameter estimation of different distributions, correlation analysis (parametric and nonparametric), regression analysis, optimal allocation of resources in partial research, exploration of response surfaces, design of experiments, efficiency tests, reliability theory, survival analysis are the most known methods of statistical analysis in which we find optimization techniques. The paper contains a synthetic presentation of the main statistical methods using classical optimization techniques, numerical optimization methods, linear and nonlinear programming, variational calculus techniques. Also, an example of applying the “simplex” algorithm in making a decision to invest an amount on the stock exchange, using a prediction model..

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VASYLKIVSKYI, Mikola, Andrii PRYKMETA, Andrii OLIYNYK, and Diana NIKITOVYCH. "OPTIMIZATION OF INTELLIGENT TELECOMMUNICATION NETWORKS." Herald of Khmelnytskyi National University. Technical sciences 217, no. 1 (February 23, 2023): 33–41. http://dx.doi.org/10.31891/2307-5732-2023-317-1-33-41.

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The paper presents the results of research on the use of machine learning in telecommunication networks and describes the basics of the theory of artificial intelligence. The impact of dynamic Bayesian network (DBN) and DNN on the development of many technologies, including user activity detection, channel estimation, and mobility tracking, is determined. The indicators of the effectiveness of communications based on the theory of information bottlenecks, which is at the junction of machine learning and forecasting, statistics and information theory, are considered. A neural network model that is pretrained for high-level tasks and divided into transmitter-side and receiver-side uses is investigated. The process of learning the model, which is performed after its adjustment, taking ino account the existing transmission channels, is considered. New ANN learning techniques capable of predicting or adapting to sudden changes in a wireless network, such as federated learning and multiagent reinforcement learning (MARL), are reviewed. The DBN model, which describes a system that dynamically changes or develops over time, is studied. The considered model provides constant monitoring of work and updating of the system and prediction of its behavior. Distributed forecasting of channel states and user locations as a key component in the development of reliable wireless communication systems is studied. The possibility of increasing the number of degrees of freedom of the generalized wireless channel G(E) in terms of: the physical propagation channel, the directional diagram of the antenna array and mutual influence, electromagnetic physical characteristics is substantiated. The impact of ultra-highresolution theory on the development of many technologies, including localization algorithms, compressed sampling, and wireless imaging algorithms, is also identified. Mathematical expressions for optimizing the functional characteristics of 5G/6G radio networks are presented using new, sufficiently formal and at the same time universal mathematical tools with an emphasis on deep learning technologies, which allow systematic, reliable and interpretable analysis of large random networks and a wide range of their network models and practical networks.

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Gaitsgory, V. A., and A. A. Pervozvanskii. "Perturbation theory for mathematical programming problems." Journal of Optimization Theory and Applications 49, no. 3 (June 1986): 389–410. http://dx.doi.org/10.1007/bf00941069.

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Skaržauskas, Valentinas, Dovilė Merkevičiūtė, and Juozas Atkočiūnas. "LOAD OPTIMIZATION OF ELASTIC-PLASTIC FRAMES AT SHAKEDOWN/PRISITAIKANČIŲ TAMPRIAI PLASTIŠKŲ RĖMŲ APKROVOS OPTIMIZACIJA." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 7, no. 6 (December 31, 2001): 433–40. http://dx.doi.org/10.3846/13921525.2001.10531769.

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In this article the theory of mathematical programming is used, composing improved mathematical models of nonlinear problems of frame loading optimization at shakedown and performing its numerical experiment. An elastic perfectly-plastic frame is considered. Frame geometry, material, load application places are considered known. Time independent load variation bounds are variable (history of loading is unknown). Mathematical model of load variation bounds optimization problem includes strength and stiffness constrains. The mentioned optimization load combines two problems. First problem is connected with the distribution of statically admissible moments at shakedown. This is a problem of residual bending moments analysis which is presented in two ways. In the first case it is formulated as a quadratic programming problem, where the objective function is non-linear, but the objective function of load optimization problem remains linear. The problem is solved by iterations, influential matrixes of residual displacements, and stresses are used. In next case, the equations of problem analysis and dependences are presented according to complete equation system of plasticity theory. Then the objective function of optimization problem becomes non-linear and it is solved in single stage. Solving the second problem, we check if it is possible to satisfy frame rigidity constrains, which are inferior or superior limits of residual displacement. This is considered as a linear programming problem. Mathematical model of frame load optimization problem at shakedown was made with the help of non-linear mathematical programming theory. Numerical experiment was realized with Rozen's gradients projecting method and using the penalty function techniques. Mathematical programming complementarity conditions prohibit taking into account the dechargable phenomena in some cross-sections, therefore analysis of residual deformation compatibility equations are performed, using linear mathematical programming.

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Qian, Xue Yi. "The Multi-Objective Optimization for Cycloidal Gear Drive Based on the Elastohydrodynamic Lubrication Theory." Advanced Materials Research 591-593 (November 2012): 697–703. http://dx.doi.org/10.4028/www.scientific.net/amr.591-593.697.

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For improving the designed quality of the cycloidal gear planetary drive, the paper derives a calculation formula of the minimum film thickness, which is between cycloidal gear teeth, based on elastohydrodynamic lubrication theory and gear geometry. A mathematical model for constrained multi-objective optimization is established and the model satisfies three constrains:maximize minimum film thickness between gear teeth( minimize the reciprocal ), minimize average value of m points’s absolute error value on active section that is between the tooth curves of positive shift optimal combination and tooth curves of rotated angle’s modification, minimize the total volume of gear drive. The paper abandons traditional designed method of the multi-objective optimization , improves two-objective particle swarm optimization and offers a new designed model for constrained three-objective optimization. The example is analyzed and the optimization program is complied using Matlab. The optimization’s process and result shows that the method of improved constrained multi-objective particle swarm optimization could effectively improve the products’ synthesize economical and technical indexes.

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Hwang, Ming-Lang Tun, Wi-Lang Collin, and Lee Sen Wang-xu. "Quantum computing and supply chain optimization: addressing complexity and efficiency challenges." International Journal of Enterprise Modelling 15, no. 3 (September 30, 2021): 148–62. http://dx.doi.org/10.35335/emod.v15i3.49.

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Quantum computing is used to address supply chain optimization complexity and efficiency. Multiple locations, time periods, transportation expenses, facility opening costs, production capacity, and demand fulfillment requirements complicate supply chains. Supply chain optimization's complexity and huge solution areas challenge traditional optimization methods. Quantum algorithms can efficiently explore bigger solution areas in quantum computing. Starting with problem identification, this research reviews quantum computing and supply chain optimization literature. The supply chain optimization problem is modeled mathematically to incorporate transportation, facility opening, production, and cost. Binary choice factors and constraints ensure demand fulfillment, facility capacity limitations, and flow balance. The mathematical theory is applied numerically. The example addresses three locations, two time periods, transportation costs, demand amounts, production capacity, and facility opening costs. A proper optimization solver optimizes the decision variables to reduce total cost while meeting demand and making efficient supply chain decisions. The supply chain optimization model reduces costs and informs transportation, facility opening, and production decisions. The numerical example shows how quantum computing may optimize supply chain topologies and reduce costs. The study explains the findings, highlights gaps in the literature, and stresses the need for more research to bridge theory and practice. This study advances supply chain optimization with quantum computing. It shows how quantum computing might improve supply chain network decision-making, efficiency, and cost.

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Wang, Ke Yan, and Qi Sheng Wang. "Mathematical Model and Numerical Experiment of Photovoltaic Water Pumping System." Advanced Materials Research 772 (September 2013): 653–57. http://dx.doi.org/10.4028/www.scientific.net/amr.772.653.

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This paper presents the engineering analytical models of photovoltaic (PV) water pumping system from electronics theory, and some mathematical models of system components have been established. Studies have shown that the minimum unit water cost may not be reached only with the control strategy of maximum output power of the system. Therefore, system optimization is very necessary to reducing the capacity for every unit of pumped water, which is based on the design optimization theory and has shown its economics.

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Duan, Dingkang. "Study on Sustainable Agricultural Structure Optimization Method Based on Multiobjective Optimization Algorithm." Computational Intelligence and Neuroscience 2022 (June 13, 2022): 1–12. http://dx.doi.org/10.1155/2022/5850684.

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Agricultural sustainable development is one of the themes of human and nature harmonious coexistence. Adjusting and optimizing agricultural structure are an important direction to improve the level of agricultural sustainable development. In this paper, related research status of the sustainable development of agriculture is analyzed; it shows that there is lack of scientific theories guidance for agricultural sustainable development. In order to optimize sustainable development of agriculture industry structure, the guidance theory of and its optimization are studied. Based on multiobjective optimization theory, several key factors that affect agricultural sustainable development and the main target indexes of agricultural sustainable development are analyzed, the mathematical model of the evaluation of the sustainable development of agriculture is established, and the solution to optimize the multiobjective model is studied. Finally, the agricultural industry sustainable development in a certain area is taken as the research object in this paper; the mathematical model and solving method of agricultural sustainable development evaluation are studied; it provides a guidance to optimize the regional agricultural industrial structure and improve the quality of agricultural sustainable development.

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15

Bellomo, Nicola, Seung-Yeal Ha, and Nisrine Outada. "Towards a mathematical theory of behavioral swarms." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 125. http://dx.doi.org/10.1051/cocv/2020071.

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This paper presents a unified mathematical theory of swarms where the dynamics of social behaviors interacts with the mechanical dynamics of self-propelled particles. The term behavioral swarms is introduced to characterize the specific object of the theory which is subsequently followed by applications. As concrete examples for our unified approach, we show that several Cucker-Smale type models with internal variables fall down to our framework. The second part of the paper shows how the modeling can be developed, beyond the Cucker-Smale approach. This will be illustrated with the aid of numerical simulations in swarms whose movement strategy is sensitive to individual social behaviors. Finally, the presentation looks ahead to research perspectives.

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16

Wang, Jun. "Research on the Separation Performance of Deoiling Hydrocyclones." Applied Mechanics and Materials 608-609 (October 2014): 14–18. http://dx.doi.org/10.4028/www.scientific.net/amm.608-609.14.

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This paper uses FLUENT as the researching tools of 3D numerical simulation of deoiling hydrocyclones, analysis on the geometric structure of deoiling Hydrocyclone, summed up a set of grid partition method based on the basic theory and turbulence simulation of CFD theory, to determine a reasonable mathematical model, boundary conditions, convection diffusion the discrete format and pressure velocity coupling algorithm. This paper establishes the mathematical model, calculation method and the optimization principle for the separation mechanism; it also provides basic theory and experience for studying on deoiling hydrocyclone such as separation mechanism, flow and turbulent scalar field characteristics and structure optimization design.

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17

Casesnoves, Francisco. "Genetic Algorithms for Interior Comparative Optimization of Standard BCS Parameters in Selected Superconductors and High-Temperature Superconductors." Standards 2, no. 3 (September 16, 2022): 430–48. http://dx.doi.org/10.3390/standards2030029.

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Inverse least squares numerical optimization, 3D/4D interior optimization, and 3D/4D graphical optimization software and algorithm programming have been presented in a series of previous articles on the applications of the BCS theory of superconductivity and TC dual/multiobjective optimizations. This study deals with the comparison/validation of the optimization results using several different methods, namely, classical inverse least squares (ILS), genetic algorithms (GA), 3D/4D interior optimization, and 2D/3D/4D graphical optimization techniques. The results comprise Tikhonov regularization algorithms and mathematical methods for all the research subjects. The findings of the mathematical programming for optimizing type I chrome isotope superconductors are validated with the genetic algorithms and compared to previous results of 3D/4D interior optimization. Additional rulings present a hypothesis of the new ‘molecular effect’ model/algorithm intended to be proven for Hg-cuprate-type high-temperature superconductors. In molecular effect optimization, inverse least squares and inverse least squares polynomial methods are applied with acceptable numerical and 2D graphical optimization solutions. For the BCS isotope effect and molecular effect, linearization logarithmic transformations for model formula software are implemented in specific programs. The solutions show accuracy with low programming residuals and confirm these findings. The results comprise two strands, the modeling for the isotope effect and molecular effect hypotheses and the development of genetic algorithms and inverse least squares-improved programming methods. Electronic physics applications in superconductors and high-temperature superconductors emerged from the rulings. Extrapolated applications for new modeling for the theory of superconductivity emerged from the numerical and image data obtained.

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Dou, Sha Sha. "Application of Intelligent Optimization Algorithm in Mechanical Design." Applied Mechanics and Materials 713-715 (January 2015): 2049–52. http://dx.doi.org/10.4028/www.scientific.net/amm.713-715.2049.

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Mechanical optimization design is a new design method in the development foundation of the modern mechanical design theory, the application of optimization design in mechanical design can make the scheme achieve some optimization results in the design requirements specified, without consuming too much computational effort. The corresponding mathematical models of ant algorithm and Cellular ant algorithm are established, according to the actual mechanical design problems, and used to solve the established mathematical model by computer, so as to obtains the optimal design scheme.

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Svaiter, B. F. "A new duality theory for mathematical programming." Optimization 60, no. 8-9 (August 2011): 1209–31. http://dx.doi.org/10.1080/02331934.2010.524217.

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Şen, Alper, Kamyar Kargar, Esma Akgün, and Mustafa Ç. Pınar. "Codon optimization: a mathematical programing approach." Bioinformatics 36, no. 13 (April 20, 2020): 4012–20. http://dx.doi.org/10.1093/bioinformatics/btaa248.

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Abstract Motivation Synthesizing proteins in heterologous hosts is an important tool in biotechnology. However, the genetic code is degenerate and the codon usage is biased in many organisms. Synonymous codon changes that are customized for each host organism may have a significant effect on the level of protein expression. This effect can be measured by using metrics, such as codon adaptation index, codon pair bias, relative codon bias and relative codon pair bias. Codon optimization is designing codons that improve one or more of these objectives. Currently available algorithms and software solutions either rely on heuristics without providing optimality guarantees or are very rigid in modeling different objective functions and restrictions. Results We develop an effective mixed integer linear programing (MILP) formulation, which considers multiple objectives. Our numerical study shows that this formulation can be effectively used to generate (Pareto) optimal codon designs even for very long amino acid sequences using a standard commercial solver. We also show that one can obtain designs in the efficient frontier in reasonable solution times and incorporate other complex objectives, such as mRNA secondary structures in codon design using MILP formulations. Availability and implementation http://alpersen.bilkent.edu.tr/codonoptimization/CodonOptimization.zip.

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FUKUSHIMA, MASAO. "HOW TO DEAL WITH UNCERTAINTY IN OPTIMIZATION — SOME RECENT ATTEMPTS." International Journal of Information Technology & Decision Making 05, no. 04 (December 2006): 623–37. http://dx.doi.org/10.1142/s0219622006002192.

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In this paper, we give a brief summary of the author's recent attempts conducted in collaboration with a number of co-authors to deal with uncertainty in various optimization problems, including complementarity problem, mathematical program with equilibrium constraints, as well as applications in data mining, mathematical finance, and game theory.

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Isenberg, Natalie M., Michael G. Taylor, Zihao Yan, Christopher L. Hanselman, Giannis Mpourmpakis, and Chrysanthos E. Gounaris. "Identification of optimally stable nanocluster geometries via mathematical optimization and density-functional theory." Molecular Systems Design & Engineering 5, no. 1 (2020): 232–44. http://dx.doi.org/10.1039/c9me00108e.

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Ehrgott, Matthias, Çiğdem Güler, Horst W. Hamacher, and Lizhen Shao. "Mathematical optimization in intensity modulated radiation therapy." 4OR 6, no. 3 (August 15, 2008): 199–262. http://dx.doi.org/10.1007/s10288-008-0083-7.

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Liu, Ping, and Hui Yi Miao. "Some Properties of Mathematical Model for Cylindricity Errors." Applied Mechanics and Materials 37-38 (November 2010): 1214–18. http://dx.doi.org/10.4028/www.scientific.net/amm.37-38.1214.

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An unconstrained optimization model, applicable to radial deviation measurement, is established for assessing cylindricity errors by the minimum circumscribed cylinder evaluation. The properties of the objective function in the optimization model are thoroughly investigated. On the basis of the modern theory of convex functions, it is strictly proved that the objective function is a continuous and non-differentiable and convex function defined on the four-dimensional Euclidean space R4. Therefore, the minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Thus, any existing optimization algorithm, so long as it is convergent, can be used to solve the objective function to get the wanted values of cylindricity errors by the minimum circumscribed cylinder assessment. An example is given to verify the theoretical results presented.

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KOLESNIK, Georgii V., and Mikhail B. RYBAKOV. "A model to optimize the structure of enterprise's fixed assets in conditions of digital transformation." Economic Analysis: Theory and Practice 20, no. 2 (February 26, 2021): 357–78. http://dx.doi.org/10.24891/ea.20.2.357.

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Subject. The article addresses the enhancement of fixed assets utilization efficiency as one of priority tasks faced by modern machine-building enterprises. Objectives. The purpose is to devise approaches and tools for solving the problems of optimization of industrial enterprises’ fixed assets development and use, on the basis of mathematical modeling. Methods. The study employs methods of mathematical modeling of economic processes, the Markov chain theory, and the multicriteria optimization. Results. We offer an approach to analyze the life cycle of enterprise’s fixed assets based on the theory of Markov chains. The paper presents a mathematical model of the fixed asset life cycle, formulates optimization tasks for fixed assets development, taking into account economic feasibility and reliability. Using the developed tools, it is possible to plan investing and operating activities for geographically distributed systems of enterprises, in particular, optimization of investment in production capacities development, planning their maintenance and repairs, load distribution between individual enterprises of the system. Conclusions. The use of modern digital technologies that provide dynamic forecasting and optimization of fixed assets enables to achieve a number of improvements, including a reduction in production time and cost and increase in efficiently used production means.

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Alawdin, Piotr, Juozas Atkociunas, and Liudas Liepa. "Optimization of the Structures at Shakedown and Rosen’s Optimality Criterion." Civil And Environmental Engineering Reports 22, no. 3 (September 1, 2016): 5–24. http://dx.doi.org/10.1515/ceer-2016-0031.

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Abstract Paper focuses on the problems of application of extreme energy principles and nonlinear mathematical programing in the theory of structural shakedown. By means of energy principles, which describes the true stress-strain state conditions of the structure, the dual mathematical models of analysis problems are formed (static and kinematic formulations). It is shown how common mathematical model of the structures optimization at shakedown with safety and serviceability constraints (according to the ultimate limit state (ULS) and serviceability limit state (SLS) requirements) on the basis of previously mentioned mathematical models is formed. The possibilities of optimization problem solution in the context of physical interpretation of optimality criterion of Rosen’s algorithm are analyzed.

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Lovianova, Iryna V., Dmytro Ye Bobyliev, and Aleksandr D. Uchitel. "Cloud calculations within the optional course Optimization Problems for 10th–11th graders." Освітній вимір 53, no. 1 (December 19, 2019): 95–110. http://dx.doi.org/10.31812/educdim.v53i1.3835.

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The article deals with the problem of introducing cloud calculations into 10th–11th graders’ training to solve optimization problems in the context of the STEM-education concept. After analyzing existing programmes of optional courses on optimization problems, the programme of the optional course Optimization Problems has been developed and substantiated implying solution of problems by the cloud environment CoCalc. It is a routine calculating operation and not a mathematical model that is accentuated in the programme. It allows considering more problems which are close to reality without adapting the material while training 10th–11th graders. Besides, the mathematical apparatus of the course which is partially known to students as the knowledge acquired from such mathematics sections as the theory of probability, mathematical statistics, mathematical analysis and linear algebra is enough to master the suggested course. The developed course deals with a whole class of problems of conventional optimization which vary greatly. They can be associated with designing devices and technological processes, distributing limited resources and planning business functioning as well as with everyday problems of people. Devices, processes and situations to which a model of optimization problem is applied are called optimization problems. Optimization methods enable optimal solutions for mathematical models. The developed course is noted for building mathematical models and defining a method to be applied to finding an efficient solution.

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Lovianova, Iryna V., Dmytro Ye Bobyliev, and Aleksandr D. Uchitel. "Cloud calculations within the optional course Optimization Problems for 10th-11th graders." CTE Workshop Proceedings 6 (March 21, 2019): 459–71. http://dx.doi.org/10.55056/cte.406.

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The article deals with the problem of introducing cloud calculations into 10th-11th graders’ training to solve optimization problems in the context of the STEM-education concept. After analyzing existing programmes of optional courses on optimization problems, the programme of the optional course Optimization Problems has been developed and substantiated implying solution of problems by the cloud environment CoCalc. It is a routine calculating operation and not a mathematical model that is accentuated in the programme. It allows considering more problems which are close to reality without adapting the material while training 10th-11th graders. Besides, the mathematical apparatus of the course which is partially known to students as the knowledge acquired from such mathematics sections as the theory of probability, mathematical statistics, mathematical analysis and linear algebra is enough to master the suggested course. The developed course deals with a whole class of problems of conventional optimization which vary greatly. They can be associated with designing devices and technological processes, distributing limited resources and planning business functioning as well as with everyday problems of people. Devices, processes and situations to which a model of optimization problem is applied are called optimization problems. Optimization methods enable optimal solutions for mathematical models. The developed course is noted for building mathematical models and defining a method to be applied to finding an efficient solution.

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Martinez, Roylan. "Optimization proposals to the payment clearing." Data Science in Finance and Economics 3, no. 1 (2023): 76–100. http://dx.doi.org/10.3934/dsfe.2023005.

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<abstract><p>In recent years, the amount of payment transactions have exponentially increased and with them, new abstract payment methods and techniques have emerged. In this paper, we provide two new interesting optimization problem solutions aimed to reduce the amount of money needed in a multilateral set-off system. The presented concepts—built upon solutions of relatively new but well-known graph theory and mathematical optimization theory—show how the use of some payment transaction methods can improve the traditional compensation logic behind a payment transaction. These theoretic optimizations solutions can lead to an increase of payment transactions of a specific market area with a common monetary union and system of payments—be it a country, a group of countries, etc—and a specific range of time —be it a year, a month, etc—. Thus, improving, in economic terms, the existing competition, economic activity and welfare.</p></abstract>

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ZAVGORODNIY, OLEXIY, DMYTRO LEVKIN, YANA KOTKO, and OLEXANDER MAKAROV. "RESEARCH OF COMPUTATIONAL MATHEMATICAL MODELS FOR TECHNICAL SYSTEMS." Herald of Khmelnytskyi National University. Technical sciences 319, no. 2 (April 27, 2023): 108–12. http://dx.doi.org/10.31891/2307-5732-2023-319-1-108-112.

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In the theory of analysis and synthesis of technical systems, mathematical modelling and optimization of multilayer systems containing sources of physical fields occupy an important place. This is due to the fact that their state is described by means of boundary value problems with multidimensional differential equations. To solve the boundary value problems and implement the process of optimizing the technical parameters of the modelled systems, it is necessary to conduct interdisciplinary studies of computational and applied optimization mathematical models. Fulfilment of the conditions for the existence of a single solution to boundary value problems by default is possible only when the object of study is a single-layer material under the action of load sources. If it is necessary to calculate and optimize the technical parameters of a multilayer material subjected to load sources, then it is impossible to immediately guarantee the correctness of the calculated and applied optimization mathematical models, since it is necessary to obtain the conditions for the existence and uniqueness of solutions to boundary value problems with systems of differential equations. Maximizing the technical parameters of load sources and averaging the characteristics of material layers will lead to approximate values of the objective function and technical parameters of the modelled system, which leads to irrational consumption of energy and heat resources and uncontrolled losses, and useless losses of the test material in the technological process. The article presents the conditions for the correctness of multipoint boundary value problems with multidimensional differential equations describing the state of a multilayer material under thermal action. It is advisable to use these studies to substantiate the correctness of other technical and biotechnological systems, which will increase the accuracy of the implementation of applied optimization problems of economic and mathematical modelling.

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KYOYA, Takashi, and Soji HIRAIDE. "OPTIMIZATION OF PATTERN OF ROCK BOLTS BASED ON THE MATHEMATICAL HOMOGENIZATION THEORY." Doboku Gakkai Ronbunshuu C 62, no. 4 (2006): 747–56. http://dx.doi.org/10.2208/jscejc.62.747.

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Sergienko, I. V., and A. A. Chikrii. "Developing B. N. Pshenichnyi’s scientific ideas in optimization and mathematical control theory." Cybernetics and Systems Analysis 48, no. 2 (March 2012): 157–79. http://dx.doi.org/10.1007/s10559-012-9395-x.

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Belegundu, Ashok D., and Jasbir S. Arora. "A study of mathematical programming methods for structural optimization. Part I: Theory." International Journal for Numerical Methods in Engineering 21, no. 9 (September 1985): 1583–99. http://dx.doi.org/10.1002/nme.1620210904.

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Medved, I., Yu Otrosh, and N. Rashkevich. "Optimization of building structures." Mechanics And Mathematical Methods 6, no. 1 (March 28, 2024): 17–25. http://dx.doi.org/10.31650/2618-0650-2024-6-1-17-25.

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In the field of the theory of calculation of building structures, there is a constant refinement of the actual operation of these structures, i.e. design schemes are created that most accurately correspond to actual operating conditions. Creating optimal structures is a very urgent task facing designers. Therefore, it is quite natural to try to solve this problem using mathematical programming methods, which involve: selecting dependent and independent variables, constructing mathematical models and establishing criteria for the effectiveness of the selected model. In this case, the model should be a function that fairly accurately describes the research being carried out using mathematical apparatus (various types of functions, equations, systems of equations and inequalities, etc.). In mathematical programming, any set of independent (controlled) variables is called a solution. Optimal solutions are those that, for one reason or another, are preferable to others. The preference (effectiveness) of the study is quantified by the numerical value of the objective function. “Solution Search” is an add-in for Microsoft Excel that is used to solve optimization problems. Simply put, with the Solver add-in, you can determine the maximum or minimum value of one cell by changing other cells. Most often, this add-in is used to find optimal solutions to problems economically. There are not enough results of using this approach for calculating building structures in the public domain. Therefore, it is quite logical to try to use this add-on in problems of optimization of building structures. In this work, an attempt was made to use mathematical programming methods and this add-on to optimize the geometric dimensions of the structure, when the numerical value of the bending moment in a specific section was chosen as an optimization criterion.

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Liu, Xiao Yang, and Xiao Guang Pei. "Mie Scattering Theory on the Rapid Detection for Milk Components." Applied Mechanics and Materials 48-49 (February 2011): 675–78. http://dx.doi.org/10.4028/www.scientific.net/amm.48-49.675.

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The scattering matrix is ill-conditioned in mathematical model used in detecting the concentration of the main components of milk, so minor error will make a large impact on the results in the process of matrix operation. This paper is about how to use POWELL optimization algorithm to calculate the particle distribution function. The algorithm uses scattering theory to realize the mathematical model to detect the milk components rapidly. The simulation and the experiment results show that this algorithm is feasible.

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Atkočiūnas, Juozas, and Algirdas Čižas. "ALEKSANDRAS ČYRAS AND OPTIMIZATION IN STRUCTURAL MECHANICS." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 8, no. 1 (March 31, 2002): 4–33. http://dx.doi.org/10.3846/13923730.2002.10531246.

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The study describes how in Lithuania (mostly in Vilnius) during some past decades a new trend of investigations in structural mechanics thanks to Aleksandras Čyras' (1927–2001) research and organisational activities has been developed. The main distinguished features of the trend are: application of mathematical programming, and especially the duality theory, to the optimization of elastic-plastic and other structures, formulation of mathematical models of structural mechanics problems, elaborating algorithms and programmes for their solution. The advantages of the research results are shown, a large information concerning the publication of the results and the evolution of investigations initiated by A. Čyras are presented.

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Bogachev, Victor, Vyacheslav Zadorozhniy, Alexandra Kravets, Taras Bogachev, and Vladimir Trapenov. "On one approach to choosing unloading stations according to egalitarian principles in transport-type optimization problems." E3S Web of Conferences 371 (2023): 05066. http://dx.doi.org/10.1051/e3sconf/202337105066.

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A multi-agent approach has been developed for solving the optimization transport-type problems. As an object of application, a multimodal system of transportation of grain cargoes with cost indicators is considered. The egalitarian principles of welfare theory implemented in the form of the Pareto criterion are used as the methodological basis of the research. A significant role belongs to the mathematical experiment as an effective tool for simulation modeling. The optimization algorithm developed in a mathematically oriented software environment makes it possible to effectively manipulate the values of cost indicators and constraints in the problem.

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Dyakov, Ivan, and Olegas Prentkovskis. "OPTIMIZATION PROBLEMS IN DESIGNING AUTOMOBILES." TRANSPORT 23, no. 4 (December 31, 2008): 316–22. http://dx.doi.org/10.3846/1648-4142.2008.23.316-322.

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A mathematical model of optimization problems in designing automobiles is suggested and requirements raised are defined taking into account the main technical and economic characteristics of the automobile. The optimality criterion of the integral parts of the automobile is presented. The system approach to the theory of parametric optimization based on generalized models is used and the algorithm for solving the considered problem is offered.

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Лащенов, Д. П. "Mathematical modeling and optimization of complexly structured objects." МОДЕЛИРОВАНИЕ, ОПТИМИЗАЦИЯ И ИНФОРМАЦИОННЫЕ ТЕХНОЛОГИИ 8, no. 4(31) (December 5, 2020): 17–18. http://dx.doi.org/10.26102/2310-6018/2020.31.4.017.

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Данная работа посвящена формализованному описанию математических моделей и оптимизационных задач сложноструктурированных объектов. В качестве объекта моделирования рассматриваются производственные системы со сложной структурой, включающей взаимодействие подсистем двух основных типов: «обработка» и «сборка». Представлен анализ специфики функционирования сложноструктурированных производственных систем. Предложен способ формализованного описания математических моделей технологических процессов обработки и сборки на основе теории массового обслуживания с применением аппарата имитационного моделирования. Принципиальным отличием математического описания подсистемы типа «сборка» от подсистемы типа «обработка» заключается в том, что для выполнения процесса сборки требуется поступление на вход устройства заданного количества заявок с разных потоков, что означает наличие всех необходимых комплектующих. Эта особенность ограничивает применение стандартных методов теории массового обслуживания, поскольку функциональные зависимости для аналитического описания процессов типа «сборка» отсутствуют. По этой причине возникает необходимость разработки имитационных моделей сложноструктурированных объектов. При этом в математической модели производственной системы учтены случайный характер распределения параметров объектов и вероятность возникновения отказов в обслуживании заявок вследствие переполнения очереди на ожидание. Рассмотрена оптимизационная задача поиска оптимальной структуры системы при ограничениях на заданное количество полученных деталей в течение определенного периода времени, а также на максимальную емкость входного накопителя и объем производственных ресурсов. This work is devoted to the formalized description of mathematical models and optimization problems of complex-structured objects. As an object of modeling, we consider production systems with a complex structure, including the interaction of subsystems of two main types: "processing" and "assembly". An analysis of the specifics of the functioning of complex-structured production systems is presented. A method is proposed for the formalized description of mathematical models of technological processes of processing and assembly based on the theory of queuing using the apparatus of simulation. The fundamental difference between the mathematical description of a subsystem of the "assembly" type and a subsystem of the "processing" type is that to complete the assembly process, a given number of applications from different streams must be received at the input of the device, which means that all the necessary components are available. This feature limits the use of standard methods of queuing theory, since there are no functional dependencies for the analytical description of processes of the "assembly" type. For this reason, it becomes necessary to develop simulation models of complexly structured objects. At the same time, the mathematical model of the production system takes into account the random nature of the distribution of the parameters of objects and the probability of refusals in servicing applications due to overflow of the waiting queue. The optimization problem of finding the optimal structure of the system is considered under restrictions on a given number of parts obtained within a certain period of time, as well as on the maximum capacity of the input storage and the volume of production resources.

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Armstrong, Ronald D., Douglas H. Jones, and Zhaobo Wang. "Optimization of Classical Reliability in Test Construction." Journal of Educational and Behavioral Statistics 23, no. 1 (March 1998): 1–17. http://dx.doi.org/10.3102/10769986023001001.

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This article considers the problem of generating a test from an item bank using a criterion based on classical test theory parameters. A mathematical programming model is formulated that maximizes the reliability coefficient α, subject to logical constraints on the choice of items. The special structure of the problem is exploited with network theory and Lagrangian relaxation techniques. An empirical study shows that the method produces tests with high coefficient a subject to various practicable item constraints.

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Michal Holdy and Juraj Beniak. "Topological optimization processes." Global Journal of Engineering and Technology Advances 10, no. 1 (January 30, 2022): 094–99. http://dx.doi.org/10.30574/gjeta.2022.10.1.0023.

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The method of topological optimization is based on a mathematical algorithm, which is based on the distribution and intensity of detail stress on the investigated component. It was developed using the Rhino-Grasshopper theory. This is a complicated FEM analysis with the help of the Nastran solver in the Siemens NX software environment. The topology detail is controlled by the degree of iteration of the algorithm, changing the size and distribution of the elements in relation to the incoming force stresses of the FEM simulation. The goal of topological optimization is a clearly defined shape of the component for a given design solution.

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Menzhinski, A. B., A. N. Malashin, and P. B. Menzhinski. "Development of Refined Electromagnetic Models of Reciprocating Electric Generators with Permanent Magnets." ENERGETIKA. Proceedings of CIS higher education institutions and power engineering associations 64, no. 4 (July 21, 2021): 291–302. http://dx.doi.org/10.21122/1029-7448-2021-64-4-291-302.

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The analysis of scientific papers devoted to the mathematical description of electric generators of reciprocating motion with permanent magnets demonstrated that the proposed mathematical models of this type of generators are based on the theory of magnetic circuits. Such mathematical models are based on a simplified representation of the magnetic system and the magnetic field in the form of a magnetic circuit with corresponding magnetic conductivities. However, unlike traditional rotary type electric machines, electric generators of reciprocating motion have a number of features, the omission of which in mathematical modeling causes the increase of the cost of their creation (due to the duration of the design and experimental refinement of the generators). Therefore, at the initial stages of electromagnetic calculation and solving optimization problems, it is necessary to use adequate mathematical models to improve the accuracy of calculations of the parameters of these generators. For this purpose, a mathematical model based on field theory can be used; however, its main drawback is the complexity of its application for solving optimization problems. In this regard, to improve the accuracy of calculations of the parameters of electric generators of reciprocating motion with permanent magnets, it is proposed to use refining coefficients (coefficients of scattering and buckling of the magnetic flux) in mathematical models based on the theory of magnetic circuits. The authors have developed refined electromagnetic models of electric generators of reciprocating motion with permanent magnets, which make it possible to obtain the main parameters of generators at the initial stages of electromagnetic calculation and when solving optimization problems with acceptable accuracy. A distinctive feature of the refined electromagnetic models of generators is the consideration of the scattering and buckling coefficients of the magnetic flux in the magnetic system that change during the simulation.

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Sasaki, Shinobu. "New approaches to manipulator arm solutions via unconstrained optimization theory." Robotica 11, no. 3 (May 1993): 253–62. http://dx.doi.org/10.1017/s026357470001612x.

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SUMMARYIn this study, highly practical and reliable methods are proposed to determine arm solutions for a six-link robot manipulator. Based on a typical mathematical structure of minimizing an objective function, the optimization theory is applied to solve a reduced system of kinematic equations. The performance tests show that three different approaches are superior to a conventional method and of sufficiently practical use. Especially, the use of an algorithm presented in a linear search is promising.

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Montoya, Germán A., and Yezid Donoso. "Delay-Sensitive Optimization Models and Distributed Routing Algorithms for Mobile Wireless Sensor Networks." International Journal of Computers Communications & Control 11, no. 6 (October 17, 2016): 819. http://dx.doi.org/10.15837/ijccc.2016.6.2745.

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Communication disruptions caused by mobility in wireless sensor networks introduce undesired delays which affect the network performance in delay sensitive applications in MWSN. In order to study the negative effects caused by mobility, we propose two mathematical models to find the minimum cost path between a source node and a destination node considering the nodes position changes across time. Our mathematical models consider the usage of buffers in the nodes to represent the fact of storing a message if there is not an appropriate forwarding node for transmitting it. In order to contrast our mathematical models results we have designed two kinds of algorithms: the first one takes advantage of the closest neighbours to the destination node in order to reach it as fast as possible from the source node. The second one simply reaches the destination node if a neighbour node is precisely the destination node. Finally, we compare the delay performance of these algorithms against our mathematical models to show how efficient they are for reaching a destination node. This paper is an extension of [10].a The mathematical model proposed in [10] is improved by adding two new binary variables with the aim of make it more readable and compact mathematically. This means a post-processing algorithm is added only for evaluating if a solution is at the first network state.

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Jafari, Hossein, Elham Bakhsheshi, and Amir-Reza Feizi-Derakhshi. "Presenting a Mathematical Programming Model for Discovering Eulerian Paths (EP) in Certain Specific Graphs." International Journal of Innovation in Engineering 3, no. 2 (June 23, 2023): 1–7. http://dx.doi.org/10.59615/ijie.3.2.1.

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In the modern era, graph theory is considered a useful tool for quantification and simplification of various dynamic components in complex systems. By representing elements as nodes and their connections as edges, graph theory can transform anything from urban planning to computer data into a meaningful mathematical language. Nowadays, numerous practical applications have been designed and developed based on graph theory. Graph theory is a branch of discrete mathematics that aims to describe and solve problems with discrete structures using points and edges. One of the problems concerning graphs is the Eulerian path problem. This research demonstrates that this problem can also be investigated from the perspective of Operations Research (OR). In a more general sense, the Eulerian path problem is a routing problem. This paper presents a pure mathematical model to describe the relationship between the variables of the Eulerian path problem. One of the features of the proposed mathematical model is its solvability by most optimization software. Finally, several numerical examples are provided to enhance the understanding of this model, and they are solved using the proposed approach. All the analyses in this research are conducted using one of the most advanced optimization software, MATLAB. The proposed mathematical model provides a systematic and efficient approach to discover Eulerian paths in specific graphs, contributing to the advancement of graph theory and its practical applications.

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Zhang, Yan Chao, and Guo Ding Chen. "Optimization Design of Finger Seal Performances Based on Game Theory." Advanced Materials Research 156-157 (October 2010): 1275–80. http://dx.doi.org/10.4028/www.scientific.net/amr.156-157.1275.

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To reach the expecting goal of lower leakage ratio and longer operation life(lower wear ratio) for finger seal, great efforts have been made continuously to obtain good structure of finger seal with advanced optimization design technology. A cooperation Nash equilibrium mathematical model of multi-objective optimization for finger seal is presented in current work based on Nash equilibrium of game theory. In this solution, the reciprocal of leakage ratio and the wear ratio value for finger seal are thought as the payoff functions and the game is solved by genetic algorithm. The numerical simulation in the paper shows that the finger seal with better performances can be achieved by using Nash equilibrium method. This means Nash equilibrium method can be used as a new multi-objective optimization method for finger seal performances optimization.

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Zhao, Xiaoying, and Dunxin Bian. "Currents’-Physical-Component-Based Reactive Power Compensation Optimization in Three-Phase, Four-Wire Systems." Applied Sciences 14, no. 12 (June 10, 2024): 5043. http://dx.doi.org/10.3390/app14125043.

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In this paper, we aim to address the limited capacity of compensation devices by enhancing their utilization rate by applying the currents’ physical component (CPC) theory for reactive power optimization in three-phase four-wire systems. When reactive currents cannot be fully compensated for, we propose using CPC theory to generate reference currents for the compensation devices. Weight coefficients associated with different reactive current components are introduced, enabling flexible combinations of these independent current components. The maximum output amplitude of the three-phase current from the compensation device serves as a constraint condition, allowing for the calculation of reference currents under various compensation targets. Additionally, a reactive current optimization compensation scheme focusing on loss reduction is selected. The simulated annealing–particle swarm optimization (SA-PSO) hybrid algorithm is employed to solve the optimization mathematical model. The discussed calculations, current waveforms, and voltage waveforms are generated using the constructed mathematical model and then used for a theoretical explanation. The simulation verifies the feasibility of the proposed method.

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Ma, Shao Jun. "Using the Theory of Spline Function to Implement the Optimal Dispatch for Mechanical Arm." Advanced Materials Research 705 (June 2013): 237–40. http://dx.doi.org/10.4028/www.scientific.net/amr.705.237.

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The researching about mechanical arm in Chinese domestic is still in the initial stage, therefore this topic is selected. The researching is doing from two aspects, they are theoretical analyzing and empirical analyzing. Through using the theory of spline and the theory of optimization, establish the mathematical model. Then in the empirical researching, the mathematical model is used. After a series of empirical tests, the correct of theoretical analyzing and empirical analyzing is confirmed.

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Xuefeng, Wang, and Mimi Chen. "Application of Mathematical Model Based on Optimization Theory and Particle Swarm Algorithm in Radar Station Layout Optimization." Journal of Physics: Conference Series 1848, no. 1 (April 1, 2021): 012087. http://dx.doi.org/10.1088/1742-6596/1848/1/012087.

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Chen, Gang, and Yu Fei Ma. "Robust Optimization Design for Spring." Applied Mechanics and Materials 190-191 (July 2012): 1376–79. http://dx.doi.org/10.4028/www.scientific.net/amm.190-191.1376.

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In here, a robust optimization mathematical model of the spring is presented. To minimize the error and maximal variations of spring stiffness coefficient related with structure parameters and its tolerances is chosen as its objective function, and the acceptable region is formed by some constraints. The theory is applied to the structure design of the closeing spring of spring actuator, the closeing characteristics are all satisfied at the optimum structure parameters, and the optimization results are discussed.

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