Relevant bibliographies by topics / Optimization (Mathematical Theory)

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Optimization (Mathematical Theory)'

Author: Grafiati
Published: 4 June 2021
Last updated: 31 July 2024

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

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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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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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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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Dissertations / Theses on the topic "Optimization (Mathematical Theory)"

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Fukasawa, Ricardo. "Single-row mixed-integer programs : theory and computations /." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24660.

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Thesis (Ph.D.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2009.
Committee Chair: William J. Cook; Committee Member: Ellis Johnson; Committee Member: George Nemhauser; Committee Member: Robin Thomas; Committee Member: Zonghao Gu
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Luo, Min. "Perturbation analysis and optimization of fork-join queueing networks." Diss., Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/14901.

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Hearnes, Warren E. II. "Near-optimal intelligent control for continuous set-point regulator problems via approximate dynamic programming." Diss., Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/24882.

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Wong, Man-kwun, and 黃文冠. "Some sensitivity results for time-delay optimal control problems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31223655.

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Elhedhli, Samir. "Interior-point decomposition methods for integer programming : theory and application." Thesis, McGill University, 2001. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=37887.

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Mixed integer programming (MIP) provides an important modeling and decision support tool for a wide variety of real-life problems. Unfortunately, practical MIPs are large-scale in size and pose serious difficulties to the available solution methodology and software.
This thesis presents a novel solution approach for large-scale mixed integer programming that integrates three bodies of research: interior point methods, decomposition techniques and branch-and-bound approaches. The combination of decomposition concepts and branch-and-bound is commonly known as branch-and-price, while the integration of decomposition concepts and interior point methods lead to the analytic centre cutting plane method (ACCPM). Unfortunately, the use of interior point methods within branch-and-bound methods could not compete with simplex based branch-and-bound due to the inability of "warm" starting.
The motivation for this study stems from the success of branch-and-price and ACCPM in solving integer and non-differentiable optimization problems respectively and the quest for a method that efficiently integrates interior-point methods and branch-and-bound.
The proposed approach is called an Interior Point Branch-and-Price method (IP-B&P) and works as follows. First, a problem's structure is exploited using Lagrangean relaxation. Second, the resulting master problem is solved using ACCPM. Finally, the overall approach is incorporated within a branch-and-bound scheme. The resulting method is more than the combination of three different techniques. It addresses and fixes complications that arise as a result of this integration. This includes the restarting of the interior-point methods, the branching rule and the exploitation of past information as a warm start.
In the first part of the thesis, we give the details of the interior-point branch-and-price method. We start by providing, discussing and implementing new ideas within ACCPM, then detail the IP-B&P method and its different components. To show the practical applicability of IP-B&P, we use the method as a basis for a new solution methodology for the production-distribution system design (PDSD) problem in supply chain management. In this second part of the thesis, we describe a two-level Lagrangean relaxation heuristic for the PDSD. The numerical results show the superiority of the method in providing the optimal solution for most of the problems attempted.
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Lam, Yun-sang Albert, and 林潤生. "Theory of optimization and a novel chemical reaction-inspired metaheuristic." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2009. http://hub.hku.hk/bib/B4322412X.

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Lam, Yun-sang Albert. "Theory of optimization and a novel chemical reaction-inspired metaheuristic." Click to view the E-thesis via HKUTO, 2009. http://sunzi.lib.hku.hk/hkuto/record/B4322412X.

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Li, Xinxin. "Some operator splitting methods for convex optimization." HKBU Institutional Repository, 2014. https://repository.hkbu.edu.hk/etd_oa/43.

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Many applications arising in various areas can be well modeled as convex optimization models with separable objective functions and linear coupling constraints. Such areas include signal processing, image processing, statistical learning, wireless networks, etc. If these well-structured convex models are treated as generic models and their separable structures are ignored in algorithmic design, then it is hard to effectively exploit the favorable properties that the objective functions possibly have. Therefore, some operator splitting methods have regained much attention from different areas for solving convex optimization models with separable structures in different contexts. In this thesis, some new operator splitting methods are proposed for convex optimiza- tion models with separable structures. We first propose combining the alternating direction method of multiplier with the logarithmic-quadratic proximal regulariza- tion for a separable monotone variational inequality with positive orthant constraints and propose a new operator splitting method. Then, we propose a proximal version of the strictly contractive Peaceman-Rachford splitting method, which was recently proposed for the convex minimization model with linear constraints and an objective function in form of the sum of two functions without coupled variables. After that, an operator splitting method suitable for parallel computation is proposed for a convex model whose objective function is the sum of three functions. For the new algorithms, we establish their convergence and estimate their convergence rates measured by the iteration complexity. We also apply the new algorithms to solve some applications arising in the image processing area; and report some preliminary numerical results. Last, we will discuss a particular video processing application and propose a series of new models for background extraction in different scenarios; to which some of the new methods are applicable. Keywords: Convex optimization, Operator splitting method, Alternating direction method of multipliers, Peaceman-Rachford splitting method, Image processing
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Achmatowicz, Richard L. (Richard Leon). "Optimal control problems on an infinite time horizon." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66052.

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李澤康 and Chak-hong Lee. "Nonlinear time-delay optimal control problem: optimality conditions and duality." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1995. http://hub.hku.hk/bib/B31212475.

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Books on the topic "Optimization (Mathematical Theory)"

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Dingzhu, Du, Pardalos P. M. 1954-, and Wu Weili, eds. Mathematical theory of optimization. Dordrecht: Kluwer Academic, 2001.

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Du, Ding-Zhu, Panos M. Pardalos, and Weili Wu, eds. Mathematical Theory of Optimization. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4757-5795-8.

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Du, Dingzhu. Mathematical Theory of Optimization. Boston, MA: Springer US, 2001.

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Baillieul, J. Mathematical Control Theory. New York, NY: Springer New York, 1999.

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Jongen, H. Th. Optimization theory. Boston: Kluwer Academic Publishers, 2004.

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Sawaragi, Yoshikazu. Theory of multiobjective optimization. Orlando: Academic Press, 1985.

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Forst, Wilhelm. Optimization: Theory and practice. New York: Springer, 2010.

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Frenk, Hans. High Performance Optimization. Boston, MA: Springer US, 2000.

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Fang, Shu-Cherng. Entropy optimization and mathematical programming. Boston: Kluwer Academic Publishers, 1997.

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Pardalos, Panos, Michael Khachay, and Alexander Kazakov, eds. Mathematical Optimization Theory and Operations Research. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-77876-7.

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Book chapters on the topic "Optimization (Mathematical Theory)"

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Lin, Shih-Chun, Tsung-Hui Chang, Eduard Jorswieck, and Pin-Hsun Lin. "Distributed Mathematical Optimization." In Information Theory, Mathematical Optimization, and Their Crossroads in 6G System Design, 175–90. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-2016-5_5.

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Lin, Shih-Chun, Tsung-Hui Chang, Eduard Jorswieck, and Pin-Hsun Lin. "Centralized Mathematical Optimization." In Information Theory, Mathematical Optimization, and Their Crossroads in 6G System Design, 145–74. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-2016-5_4.

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Bloch, Anthony M., and Peter E. Crouch. "Optimal Control, Optimization, and Analytical Mechanics." In Mathematical Control Theory, 268–321. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-1416-8_8.

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Chakrabarty, Siddhartha Pratim, and Ankur Kanaujiya. "Bond Portfolio Optimization." In Mathematical Portfolio Theory and Analysis, 117–31. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-19-8544-7_8.

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Cortés, Jorge, and Sonia Martínez. "Distributed Line Search for Multiagent Convex Optimization." In Mathematical Control Theory I, 95–110. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-20988-3_6.

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Cardinal, Jean, Samuel Fiorini, and Gwenaël Joret. "Minimum Entropy Combinatorial Optimization Problems." In Mathematical Theory and Computational Practice, 79–88. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03073-4_9.

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Halanay, Aristide, and Judita Samuel. "Some Unconstrained Dynamic Optimization Problems." In Mathematical Modelling: Theory and Applications, 270–305. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-015-8915-4_9.

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Kohlas, Jürg. "The mathematical theory of evidence — A short introduction." In System Modelling and Optimization, 37–53. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-0-387-34897-1_4.

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Ioffe, Alexander. "Towards Metric Theory of Metric Regularity." In Approximation, Optimization and Mathematical Economics, 165–76. Heidelberg: Physica-Verlag HD, 2001. http://dx.doi.org/10.1007/978-3-642-57592-1_15.

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Shi, Bin, and S. S. Iyengar. "Optimization Formulation." In Mathematical Theories of Machine Learning - Theory and Applications, 17–28. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-17076-9_3.

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Conference papers on the topic "Optimization (Mathematical Theory)"

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Zhang, Yue, Yunke Zhang, and Wanlong Xu. "Network planning model analysis based on mathematical optimization theory." In 2016 International Conference on Communication and Electronics Systems (ICCES). IEEE, 2016. http://dx.doi.org/10.1109/cesys.2016.7889914.

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Pauline, Ong, Ong Kok Meng, and Sia Chee Kiong. "An improved flower pollination algorithm with chaos theory for function optimization." In PROCEEDINGS OF THE 24TH NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES: Mathematical Sciences Exploration for the Universal Preservation. Author(s), 2017. http://dx.doi.org/10.1063/1.4995922.

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"Inverse and Optimization Problems." In 10th International Conference on Mathematical Methods in Electromagnetic Theory, 2004. IEEE, 2004. http://dx.doi.org/10.1109/mmet.2004.1397075.

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Kubytskyi, Viacheslav, Bernard Sapoval, Gwenael Dun, and Jean-Francois Rosnarho. "Fast optimization of microwave absorbers." In 2012 International Conference on Mathematical Methods in Electromagnetic Theory (MMET). IEEE, 2012. http://dx.doi.org/10.1109/mmet.2012.6331169.

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Bader-El-Den, Mohamed, and Todd Perry. "Mathematical function optimization using a novel algorithm based on Newtonian field theory." In 2016 IEEE Congress on Evolutionary Computation (CEC). IEEE, 2016. http://dx.doi.org/10.1109/cec.2016.7748343.

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Shevchenko, Halyna, Nataliia Dakhno, Olga Leshchenko, Oleg Barabash, Yuri Kravchenko, and Andriy Dudnik. "Using Mathematical Optimization Methods to Maximize Audience Reach with Budget Constraints." In 2022 IEEE 4th International Conference on Advanced Trends in Information Theory (ATIT). IEEE, 2022. http://dx.doi.org/10.1109/atit58178.2022.10024187.

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Mishkevich, Victor. "Design of Marine Propellers Using Vortex Theory: Theory and Practice." In SNAME 7th Propeller and Shafting Symposium. SNAME, 1994. http://dx.doi.org/10.5957/pss-1994-014.

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The applications of vortex theory lo propeller design is discussed New approach is based on an improved mathematical model of the propeller, including optimization of circulation distribution with restrictions; prescribing of velocity distribution separately for suction and pressure sides of blade; viscosity effect corrections.
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Boruhovich, S., and A. Gribovsky. "Geometry optimization of periodic screen cell with two orthogonal rectangular waveguides." In 2008 International Conference on Mathematical Methods in Electromagnetic Theory (MEET). IEEE, 2008. http://dx.doi.org/10.1109/mmet.2008.4581057.

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Donets, I. V., A. A. Peretyatko, and S. M. Tsvetkovskaya. "Direction pattern optimization for circular antenna array in the presence of intense clutter." In 2012 International Conference on Mathematical Methods in Electromagnetic Theory (MMET). IEEE, 2012. http://dx.doi.org/10.1109/mmet.2012.6331152.

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Yeliseyeva, N., and N. Gorobets. "Optimization of radiation characteristics of wire antenna with finite size plane, V - and Π - figuration corner reflectors." In 2012 International Conference on Mathematical Methods in Electromagnetic Theory (MMET). IEEE, 2012. http://dx.doi.org/10.1109/mmet.2012.6331151.

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Reports on the topic "Optimization (Mathematical Theory)"

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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. [б. в.], September 2019. http://dx.doi.org/10.31812/123456789/3267.

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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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Semerikov, Serhiy O., Illia O. Teplytskyi, Yuliia V. Yechkalo, and Arnold E. Kiv. Computer Simulation of Neural Networks Using Spreadsheets: The Dawn of the Age of Camelot. [б. в.], November 2018. http://dx.doi.org/10.31812/123456789/2648.

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The article substantiates the necessity to develop training methods of computer simulation of neural networks in the spreadsheet environment. The systematic review of their application to simulating artificial neural networks is performed. The authors distinguish basic approaches to solving the problem of network computer simulation training in the spreadsheet environment, joint application of spreadsheets and tools of neural network simulation, application of third-party add-ins to spreadsheets, development of macros using the embedded languages of spreadsheets; use of standard spreadsheet add-ins for non-linear optimization, creation of neural networks in the spreadsheet environment without add-ins and macros. After analyzing a collection of writings of 1890-1950, the research determines the role of the scientific journal “Bulletin of Mathematical Biophysics”, its founder Nicolas Rashevsky and the scientific community around the journal in creating and developing models and methods of computational neuroscience. There are identified psychophysical basics of creating neural networks, mathematical foundations of neural computing and methods of neuroengineering (image recognition, in particular). The role of Walter Pitts in combining the descriptive and quantitative theories of training is discussed. It is shown that to acquire neural simulation competences in the spreadsheet environment, one should master the models based on the historical and genetic approach. It is indicated that there are three groups of models, which are promising in terms of developing corresponding methods – the continuous two-factor model of Rashevsky, the discrete model of McCulloch and Pitts, and the discrete-continuous models of Householder and Landahl.
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Ratmanski, Kiril, and Sergey Vecherin. Resilience in distributed sensor networks. Engineer Research and Development Center (U.S.), October 2022. http://dx.doi.org/10.21079/11681/45680.

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With the advent of cheap and available sensors, there is a need for intelligent sensor selection and placement for various purposes. While previous research was focused on the most efficient sensor networks, we present a new mathematical framework for efficient and resilient sensor network installation. Specifically, in this work we formulate and solve a sensor selection and placement problem when network resilience is also a factor in the optimization problem. Our approach is based on the binary linear programming problem. The generic formulation is probabilistic and applicable to any sensor types, line-of-site and non-line-of-site, and any sensor modality. It also incorporates several realistic constraints including finite sensor supply, cost, energy consumption, as well as specified redundancy in coverage areas that require resilience. While the exact solution is computationally prohibitive, we present a fast algorithm that produces a near-optimal solution that can be used in practice. We show how such formulation works on 2D examples, applied to infrared (IR) sensor networks designed to detect and track human presence and movements in a specified coverage area. Analysis of coverage and comparison of sensor placement with and without resilience considerations is also performed.
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