Log in

Relevant bibliographies by topics / Mathematical optimization. Programming (Mathematics) Convex programming / Journal articles

To see the other types of publications on this topic, follow the link: Mathematical optimization. Programming (Mathematics) Convex programming.

Journal articles on the topic 'Mathematical optimization. Programming (Mathematics) Convex programming'

Author: Grafiati

Published: 4 June 2021

Last updated: 10 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Mathematical optimization. Programming (Mathematics) Convex programming.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Ceria, Sebastián, and João Soares. "Convex programming for disjunctive convex optimization." Mathematical Programming 86, no. 3 (December 1, 1999): 595–614. http://dx.doi.org/10.1007/s101070050106.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Fu, J. Y., and Y. H. Wang. "Arcwise Connected Cone-Convex Functions and Mathematical Programming." Journal of Optimization Theory and Applications 118, no. 2 (August 2003): 339–52. http://dx.doi.org/10.1023/a:1025451422581.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

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

Full text

Abstract:

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).

APA, Harvard, Vancouver, ISO, and other styles

4

Zhou, XueGang, and JiHui Yang. "Global Optimization for the Sum of Concave-Convex Ratios Problem." Journal of Applied Mathematics 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/879739.

Full text

Abstract:

This paper presents a branch and bound algorithm for globally solving the sum of concave-convex ratios problem (P) over a compact convex set. Firstly, the problem (P) is converted to an equivalent problem (P1). Then, the initial nonconvex programming problem is reduced to a sequence of convex programming problems by utilizing linearization technique. The proposed algorithm is convergent to a global optimal solution by means of the subsequent solutions of a series of convex programming problems. Some examples are given to illustrate the feasibility of the proposed algorithm.

APA, Harvard, Vancouver, ISO, and other styles

5

Thuy, Le Quang, Nguyen Thi Bach Kim, and Nguyen Tuan Thien. "Generating Efficient Outcome Points for Convex Multiobjective Programming Problems and Its Application to Convex Multiplicative Programming." Journal of Applied Mathematics 2011 (2011): 1–21. http://dx.doi.org/10.1155/2011/464832.

Full text

Abstract:

Convex multiobjective programming problems and multiplicative programming problems have important applications in areas such as finance, economics, bond portfolio optimization, engineering, and other fields. This paper presents a quite easy algorithm for generating a number of efficient outcome solutions for convex multiobjective programming problems. As an application, we propose an outer approximation algorithm in the outcome space for solving the multiplicative convex program. The computational results are provided on several test problems.

APA, Harvard, Vancouver, ISO, and other styles

6

Xu, Z. K., and S. C. Fang. "Unconstrained convex programming approach to linear programming." Journal of Optimization Theory and Applications 86, no. 3 (September 1995): 745–52. http://dx.doi.org/10.1007/bf02192167.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

fang, S. C., and H. S. J. Tsao. "An unconstrained convex programming approach to solving convex quadratic programming problems." Optimization 27, no. 3 (January 1993): 235–43. http://dx.doi.org/10.1080/02331939308843884.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Senchukov, Viktor. "The solution of optimization problems in the economy by overlaying integer lattices: applied aspect." Economics of Development 18, no. 1 (June 10, 2019): 44–55. http://dx.doi.org/10.21511/ed.18(1).2019.05.

Full text

Abstract:

The results of generalization of scientific approaches to the solution of modern economic optimization tasks have shown the need for a new vision of their solution based on the improvement of existing mathematical tools. It is established that the peculiarities of the practical use of existing mathematical tools for solving economic optimization problems are caused by the problems of enterprise management in the presence of nonlinear processes in the economy, which also require consideration of the corresponding characteristics of nonlinear dynamic processes. The approach to solving the problem of integer (discrete) programming associated with the difficulties that arise when applying precise methods (methods of separation and combinatorial methods) is proposed, namely: a fractional Gomorrhic algorithm – for solving entirely integer problems (by gradual "narrowing" areas of admissible solutions of the problem under consideration); the method of branches and borders - which involves replacing the complete overview of all plans by their partial directional over. Illustrative examples of schemes of geometric programming, fractional-linear programming, nonlinear programming with a non-convex region, fractional-nonlinear programming with a non-convex domain, and research on the optimum model of Cobb-Douglas model are given. The advanced mathematical tools on the basis of the method of overlaying integer grids (OIG), which will solve problems of purely discrete, and not only integer optimization, as an individual case, are presented in the context of solving optimization tasks of an applied nature and are more effective at the expense of reducing the complexity and duration of their solving. It is proved that appropriate analytical support should be used as an economic and mathematical tool at the stage of solving tasks of an economic nature, in particular optimization of the parameters of the processes of organization and preparation of production of new products of the enterprises of the real sector of the economy.

APA, Harvard, Vancouver, ISO, and other styles

9

Trujillo-Cortez, R., and S. Zlobec. "Bilevel convex programming models." Optimization 58, no. 8 (November 2009): 1009–28. http://dx.doi.org/10.1080/02331930701763330.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Gil-González, Walter, Oscar Danilo Montoya, Luis Fernando Grisales-Noreña, Fernando Cruz-Peragón, and Gerardo Alcalá. "Economic Dispatch of Renewable Generators and BESS in DC Microgrids Using Second-Order Cone Optimization." Energies 13, no. 7 (April 3, 2020): 1703. http://dx.doi.org/10.3390/en13071703.

Full text

Abstract:

A convex mathematical model based on second-order cone programming (SOCP) for the optimal operation in direct current microgrids (DCMGs) with high-level penetration of renewable energies and battery energy storage systems (BESSs) is developed in this paper. The SOCP formulation allows converting the non-convex model of economic dispatch into a convex approach that guarantees the global optimum and has an easy implementation in specialized software, i.e., CVX. This conversion is accomplished by performing a mathematical relaxation to ensure the global optimum in DCMG. The SOCP model includes changeable energy purchase prices in the DCMG operation, which makes it in a suitable formulation to be implemented in real-time operation. An energy short-term forecasting model based on a receding horizon control (RHC) plus an artificial neural network (ANN) is used to forecast primary sources of renewable energy for periods of 0.5h. The proposed mathematical approach is compared to the non-convex model and semidefinite programming (SDP) in three simulation scenarios to validate its accuracy and efficiency.

APA, Harvard, Vancouver, ISO, and other styles

11

Jarre, Florian. "Interior-point methods for convex programming." Applied Mathematics & Optimization 26, no. 3 (November 1992): 287–311. http://dx.doi.org/10.1007/bf01371086.

Full text

APA, Harvard, Vancouver, ISO, and other styles

12

Zarichnyi, M. "FUNCTORS AND SPACES IN IDEMPOTENT MATHEMATICS." Bukovinian Mathematical Journal 9, no. 1 (2021): 171–79. http://dx.doi.org/10.31861/bmj2021.01.14.

Full text

Abstract:

Idempotent mathematics is a branch of mathematics in which idempotent operations (for example, max) on the set of reals play a central role. In recent decades, we have seen intensive research in this direction. The principle of correspondence (this is an informal principle analogous to the Bohr correspondence principle in the quantum mechanics) asserts that each meaningful concept or result of traditional mathematics corresponds to a meaningful concept or result of idempotent mathematics. In particular, to the notion of probability measure there corresponds that if Maslov measure (also called idempotent measure) as well as more recent notion of max-min measure. Also, there are idempotent counterparts of the convex sets; these include the so-called max-plus and max min convex sets. Methods of idempotent mathematics are used in optimization problems, dynamic programming, mathematical economics, game theory, mathematical biology and other disciplines. In this paper we provide a survey of results that concern algebraic and geometric properties of the functors of idempotent and max-min measures.

APA, Harvard, Vancouver, ISO, and other styles

13

Gao, Yuelin, and Siqiao Jin. "A Global Optimization Algorithm for Sum of Linear Ratios Problem." Journal of Applied Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/276245.

Full text

Abstract:

We equivalently transform the sum of linear ratios programming problem into bilinear programming problem, then by using the linear characteristics of convex envelope and concave envelope of double variables product function, linear relaxation programming of the bilinear programming problem is given, which can determine the lower bound of the optimal value of original problem. Therefore, a branch and bound algorithm for solving sum of linear ratios programming problem is put forward, and the convergence of the algorithm is proved. Numerical experiments are reported to show the effectiveness of the proposed algorithm.

APA, Harvard, Vancouver, ISO, and other styles

14

Dong, Lei, Ai Zhong Tian, Tian Jiao Pu, Zheng Fan, and Ting Yu. "Reactive Power Optimization for Distribution Network with Distributed Generators Based on Semi-Definite Programming." Advanced Materials Research 1070-1072 (December 2014): 809–14. http://dx.doi.org/10.4028/www.scientific.net/amr.1070-1072.809.

Full text

Abstract:

Reactive power optimization for distribution network with distributed generators is a complicated nonconvex nonlinear mixed integer programming problem. This paper built a mathematical model of reactive power optimization for distribution network and a new method to solve this problem was proposed based on semi-definite programming. The original mathematical model was transformed and relaxed into a convex SDP model, to guarantee the global optimal solution within the polynomial times. Then the model was extended to a mixed integer semi-definite programming model with discrete variables when considering discrete compensation equipment such as capacitor banks. Global optimal solution of this model can be obtained by cutting plane method and branch and bound method. Numerical tests on the modified IEEE 33-bus system show this method is exact and can be solved efficiently.

APA, Harvard, Vancouver, ISO, and other styles

15

Tseng, P. "Linearly constrained convex programming as unconstrained differentiable concave programming." Journal of Optimization Theory and Applications 85, no. 2 (May 1995): 489–94. http://dx.doi.org/10.1007/bf02192238.

Full text

APA, Harvard, Vancouver, ISO, and other styles

16

Wang, Lei, and Hong Luo. "Robust Linear Programming with Norm Uncertainty." Journal of Applied Mathematics 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/209239.

Full text

Abstract:

We consider the linear programming problem with uncertainty set described byp,w-norm. We suggest that the robust counterpart of this problem is equivalent to a computationally convex optimization problem. We provide probabilistic guarantees on the feasibility of an optimal robust solution when the uncertain coefficients obey independent and identically distributed normal distributions.

APA, Harvard, Vancouver, ISO, and other styles

17

Jung, Jin Hyuk, Dianne P. O’Leary, and André L. Tits. "Adaptive constraint reduction for convex quadratic programming." Computational Optimization and Applications 51, no. 1 (March 9, 2010): 125–57. http://dx.doi.org/10.1007/s10589-010-9324-8.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Fukushima, Masao, Mounir Haddou, Hien Van Nguyen, Jean-Jacques Strodiot, Takanobu Sugimoto, and Eiki Yamakawa. "A parallel descent algorithm for convex programming." Computational Optimization and Applications 5, no. 1 (January 1996): 5–37. http://dx.doi.org/10.1007/bf00429749.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

Zillober, Ch, K. Schittkowski, and K. Moritzen. "Very large scale optimization by sequential convex programming." Optimization Methods and Software 19, no. 1 (February 2004): 103–20. http://dx.doi.org/10.1080/10556780410001647195.

Full text

APA, Harvard, Vancouver, ISO, and other styles

20

Pei, Pei, and Jiang Wang. "A New Optimal Guidance Law with Impact Time and Angle Constraints Based on Sequential Convex Programming." Mathematical Problems in Engineering 2021 (January 30, 2021): 1–15. http://dx.doi.org/10.1155/2021/6618351.

Full text

Abstract:

This paper proposed an optimal time-varying proportional navigation guidance law based on sequential convex programming. The guidance law can achieve the desired impact angle and impact time with look angle and lateral acceleration constraints. By treating the multiconstraints’ guidance problem as an optimization problem and changing the independent variable to linearize the problem and constraints, the original nonlinear and nonconvex problem is transformed into a series of convex optimization problem so that it can be quickly solved by sequential convex programming. Numerical simulations compared to nonlinear programming and traditional analytical guidance law demonstrate the effectiveness and efficiency of the proposed algorithm. Finally, the proposed guidance law is verified to satisfy different impact time periods and impact angle constraints.

APA, Harvard, Vancouver, ISO, and other styles

21

Carlone, L., V. Srivastava, F. Bullo, and G. C. Calafiore. "Distributed Random Convex Programming via Constraints Consensus." SIAM Journal on Control and Optimization 52, no. 1 (January 2014): 629–62. http://dx.doi.org/10.1137/120885796.

Full text

APA, Harvard, Vancouver, ISO, and other styles

22

Alvarez, Felipe, Jérôme Bolte, and Olivier Brahic. "Hessian Riemannian Gradient Flows in Convex Programming." SIAM Journal on Control and Optimization 43, no. 2 (January 2004): 477–501. http://dx.doi.org/10.1137/s0363012902419977.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

Glazos, Michael P., Stefen Hui, and Stanislaw H. Zak. "Sliding Modes in Solving Convex Programming Problems." SIAM Journal on Control and Optimization 36, no. 2 (March 1998): 680–97. http://dx.doi.org/10.1137/s0363012993255880.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

Goldbach, R. "Some Randomized Algorithms for Convex Quadratic Programming." Applied Mathematics and Optimization 39, no. 1 (January 2, 1999): 121–42. http://dx.doi.org/10.1007/s002459900101.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

de Oliveira, Welington. "Sequential Difference-of-Convex Programming." Journal of Optimization Theory and Applications 186, no. 3 (August 4, 2020): 936–59. http://dx.doi.org/10.1007/s10957-020-01721-x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Chen, Wei, Atul Sahai, Achille Messac, and Glynn J. Sundararaj. "Exploration of the Effectiveness of Physical Programming in Robust Design." Journal of Mechanical Design 122, no. 2 (March 1, 2000): 155–63. http://dx.doi.org/10.1115/1.533565.

Full text

Abstract:

Computational optimization for design is effective only to the extent that the aggregate objective function adequately captures designer’s preference. Physical programming is an optimization method that captures the designer’s physical understanding of the desired design outcome in forming the aggregate objective function. Furthermore, to be useful, a resulting optimal design must be sufficiently robust/insensitive to known and unknown variations that to different degrees affect the design’s performance. This paper explores the effectiveness of the physical programming approach in explicitly addressing the issue of design robustness. Specifically, we synergistically integrate methods that had previously and independently been developed by the authors, thereby leading to optimal—robust—designs. We show how the physical programming method can be used to effectively exploit designer preference in making tradeoffs between the mean and variation of performance, by solving a bi-objective robust design problem. The work documented in this paper establishes the general superiority of physical programming over other conventional methods (e.g., weighted sum) in solving multiobjective optimization problems. It also illustrates that the physical programming method is among the most effective multicriteria mathematical programming techniques for the generation of Pareto solutions that belong to both convex and non-convex efficient frontiers. [S1050-0472(00)00902-8]

APA, Harvard, Vancouver, ISO, and other styles

27

Chan, Timothy M. "Deterministic Algorithms for 2-d Convex Programming and 3-d Online Linear Programming." Journal of Algorithms 27, no. 1 (April 1998): 147–66. http://dx.doi.org/10.1006/jagm.1997.0914.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

Luo, Z. Q., J. F. Sturm, and S. Zhang. "Conic convex programming and self-dual embedding." Optimization Methods and Software 14, no. 3 (January 2000): 169–218. http://dx.doi.org/10.1080/10556780008805800.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Weir, T., and B. Mond. "Proper efficiency and duality for vector valued optimization problems." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 43, no. 1 (August 1987): 21–34. http://dx.doi.org/10.1017/s1446788700028937.

Full text

Abstract:

AbstractThe duality results of Wolfe for scalar convex programming problems and some of the more recent duality results for scalar nonconvex programming problems are extended to vector valued programs. Weak duality is established using a ‘Pareto’ type relation between the primal and dual objective functions.

APA, Harvard, Vancouver, ISO, and other styles

30

Kanno, Yoshihiro. "Robust truss topology optimization via semidefinite programming with complementarity constraints: a difference-of-convex programming approach." Computational Optimization and Applications 71, no. 2 (June 9, 2018): 403–33. http://dx.doi.org/10.1007/s10589-018-0013-3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Sumin, Mikhail Iosifovich. "WHY REGULARIZATION OF LAGRANGE PRINCIPLE AND PONTRYAGIN MAXIMUM PRINCIPLE IS NEEDED AND WHAT IT GIVES." Tambov University Reports. Series: Natural and Technical Sciences, no. 124 (2018): 757–75. http://dx.doi.org/10.20310/1810-0198-2018-23-124-757-775.

Full text

Abstract:

We consider the regularization of the classical Lagrange principle and the Pontryagin maximum principle in convex problems of mathematical programming and optimal control. On example of the “simplest” problems of constrained infinitedimensional optimization, two main questions are discussed: why is regularization of the classical optimality conditions necessary and what does it give?

APA, Harvard, Vancouver, ISO, and other styles

32

Asgharian, M., and S. Zlobec. "Convex Parametric Programming in Abstract Spaces." Optimization 51, no. 6 (August 2002): 841–61. http://dx.doi.org/10.1080/0233193021000015659.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

Voronkov, O., O. Baistryk, and A. Danylyuk. "MATHEMATICAL MODELING OF OPTIMAL HEIGHTS OF EXTERNAL GEODESIC SIGNS." Municipal economy of cities 1, no. 161 (March 26, 2021): 109–15. http://dx.doi.org/10.33042/2522-180-2021-1-161-109-115.

Full text

Abstract:

Due to the great importance of geodetic networks for the formation of a unified coordinate system on the territory of Ukraine, external geodetic signs have been established, which need to be restored and further developed. At the design stage, the calculation of the heights of geodetic signs is performed on topographic maps. The cost of erection of geodetic signs on average is 50 - 60% of the total cost of creating a geodetic network, so there is a need to pay close attention to the choice of places to build signs that provide their optimal height. The article presents a methodical approach to determining the heights of external geodetic signs, based on the mathematical apparatus used for modeling and solving optimization problems. The principle of construction of the optimization model of the problem during the design of external geodetic signs in the conditions when their direct visibility should be provided is considered. The article considers in detail the types and structures of external geodetic signs, identifies the features of their location and construction. The resulting optimization model includes objective function, which is a quadratic form, and line restriction. This model is a model of quadratic programming, that belongs to a class of nonlinear programming models, but have their particular case and the simplest of nonlinear. This is because property quadratic model, which consists in the fact that since the problem of quadratic programming set of feasible solutions is convex, then, if the objective function is concave, any local maximum is global, and if the objective function is convex, then any local minimum is also global. The necessity of solving the problem of optimizing the heights of geodetic signs is substantiated, which is still connected with the financial costs for their construction and reconstruction. It is concluded that the approach to determining the heights of external geodetic signs presented in the article, which uses a mathematical apparatus for solving optimization problems, is an effective and efficient approach, and allows to numerically justify the minimum required and sufficient height of external geodetic signs. Using the present approach to the determination of geodetic heights external signs to optimize the financial costs of their construction, which is essential.

APA, Harvard, Vancouver, ISO, and other styles

34

Oliveira, Rúbia M., and Paulo A. V. Ferreira. "A convex analysis approach for convex multiplicative programming." Journal of Global Optimization 41, no. 4 (December 21, 2007): 579–92. http://dx.doi.org/10.1007/s10898-007-9267-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

35

Hori, Yutaka, and Hiroki Miyazako. "Analysing diffusion and flow-driven instability using semidefinite programming." Journal of The Royal Society Interface 16, no. 150 (January 2019): 20180586. http://dx.doi.org/10.1098/rsif.2018.0586.

Full text

Abstract:

Diffusion and flow-driven instability, or transport-driven instability, is one of the central mechanisms to generate inhomogeneous gradient of concentrations in spatially distributed chemical systems. However, verifying the transport-driven instability of reaction–diffusion–advection systems requires checking the Jacobian eigenvalues of infinitely many Fourier modes, which is computationally intractable. To overcome this limitation, this paper proposes mathematical optimization algorithms that determine the stability/instability of reaction–diffusion–advection systems by finite steps of algebraic calculations. Specifically, the stability/instability analysis of Fourier modes is formulated as a sum-of-squares optimization program, which is a class of convex optimization whose solvers are widely available as software packages. The optimization program is further extended for facile computation of the destabilizing spatial modes. This extension allows for predicting and designing the shape of the concentration gradient without simulating the governing equations. The streamlined analysis process of self-organized pattern formation is demonstrated with a simple illustrative reaction model with diffusion and advection.

APA, Harvard, Vancouver, ISO, and other styles

36

Dolatnezhadsomarin, Azam, Esmaile Khorram, and Latif Pourkarimi. "Efficient algorithms for solving nonlinear fractional programming problems." Filomat 33, no. 7 (2019): 2149–79. http://dx.doi.org/10.2298/fil1907149d.

Full text

Abstract:

In this paper, an efficient algorithm based on the Pascoletti-Serafini scalarization (PS) approach is proposed to obtain almost uniform approximations of the entire Pareto front of bi-objective optimization problems. Five test problems with convex, non-convex, connected, and disconnected Pareto fronts are applied to evaluate the quality of approximations obtained by the proposed algorithm. Results are compared with results of some algorithms including the normal constraint (NC), weighted constraint (WC), Benson type, differential evolution (DE) with binomial crossover, non-dominated sorting genetic algorithm-II (NSGA-II), and S metric selection evolutionary multiobjective algorithm (SMS-EMOA). The results confirm the effectiveness of the presented bi-objective algorithm in terms of the quality of approximations of the Pareto front and CPU time. In addition, two algorithms are presented for approximately solving fractional programming (FP) problems. The first algorithm is based on an objective space cut and bound method for solving convex FP problems and the second algorithm is based on the proposed bi-objective algorithm for solving nonlinear FP problems. In addition, several examples are provided to demonstrate the performance of these suggested fractional algorithms.

APA, Harvard, Vancouver, ISO, and other styles

37

Chen, Liang, Xiaokai Chang, and Sanyang Liu. "A Three-Operator Splitting Perspective of a Three-Block ADMM for Convex Quadratic Semidefinite Programming and Beyond." Asia-Pacific Journal of Operational Research 37, no. 04 (May 19, 2020): 2040009. http://dx.doi.org/10.1142/s0217595920400096.

Full text

Abstract:

In recent years, several convergent variants of the multi-block alternating direction method of multipliers (ADMM) have been proposed for solving the convex quadratic semidefinite programming via its dual, which is inherently a [Formula: see text]-block separable convex optimization problem with coupled linear constraints. Among these multi-block ADMM-type algorithms, the modified [Formula: see text]-block ADMM in [Chang, XK, SY Liu and X Li (2016). Modified alternating direction method of multipliers for convex quadratic semidefinite programming. Neurocomputing, 214, 575–586] bears a peculiar feature that the augmented Lagrangian function is not necessarily to be minimized with respect to the block-variable corresponding to the quadratic term in the objective function. In this paper, we lay the theoretical foundation of this phenomenon by interpreting this modified [Formula: see text]-block ADMM as a special implementation of the Davis–Yin [Formula: see text]-operator splitting [Davis, D and WT Yin (2017). A three-operator splitting scheme and its optimization applications. Set-Valued and Variational Analysis, 25, 829–858]. Based on this perspective, we are able to extend this modified [Formula: see text]-block ADMM to a generalized [Formula: see text]-block ADMM, in the sense of [Eckstein, J and DP Bertsekas (1992). On the Douglas–Rachford splitting method and the proximal point algorithm for maximal monotone operators. Mathematical Programming, 55, 293–318], which not only applies to the more general convex composite quadratic programming problems but also admits the flexibility of achieving even better numerical performance.

APA, Harvard, Vancouver, ISO, and other styles

38

Li, Lifeng, Sanyang Liu, and Jianke Zhang. "Univex Interval-Valued Mapping with Differentiability and Its Application in Nonlinear Programming." Journal of Applied Mathematics 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/383692.

Full text

Abstract:

Interval-valued univex functions are introduced for differentiable programming problems. Optimality and duality results are derived for a class of generalized convex optimization problems with interval-valued univex functions.

APA, Harvard, Vancouver, ISO, and other styles

39

Chirre, Andrés, Valdir Pereira Júnior, and David de Laat. "Primes in arithmetic progressions and semidefinite programming." Mathematics of Computation 90, no. 331 (April 2, 2021): 2235–46. http://dx.doi.org/10.1090/mcom/3638.

Full text

Abstract:

Assuming the generalized Riemann hypothesis, we give asymptotic bounds on the size of intervals that contain primes from a given arithmetic progression using the approach developed by Carneiro, Milinovich and Soundararajan [Comment. Math. Helv. 94, no. 3 (2019)]. For this we extend the Guinand-Weil explicit formula over all Dirichlet characters modulo q ≥ 3 q \geq 3 , and we reduce the associated extremal problems to convex optimization problems that can be solved numerically via semidefinite programming.

APA, Harvard, Vancouver, ISO, and other styles

40

Kostyukova, O. I., and T. V. Tchemisova. "Sufficient optimality conditions for convex semi-infinite programming." Optimization Methods and Software 25, no. 2 (April 2010): 279–97. http://dx.doi.org/10.1080/10556780902992803.

Full text

APA, Harvard, Vancouver, ISO, and other styles

41

Kozma, Attila, Christian Conte, and Moritz Diehl. "Benchmarking large-scale distributed convex quadratic programming algorithms." Optimization Methods and Software 30, no. 1 (May 12, 2014): 191–214. http://dx.doi.org/10.1080/10556788.2014.911298.

Full text

APA, Harvard, Vancouver, ISO, and other styles

42

Kebaili, Zahira, and Mohamed Achache. "Solving nonmonotone affine variational inequalities problem by DC programming and DCA." Asian-European Journal of Mathematics 13, no. 03 (December 17, 2018): 2050067. http://dx.doi.org/10.1142/s1793557120500679.

Full text

Abstract:

In this paper, we consider an optimization model for solving the nonmonotone affine variational inequalities problem (AVI). It is formulated as a DC (Difference of Convex functions) program for which DCA (DC Algorithms) are applied. The resulting DCA are simple: it consists of solving successive convex quadratic program. Numerical experiments on several test problems illustrate the efficiency of the proposed approach in terms of the quality of the obtained solutions and the speed of convergence.

APA, Harvard, Vancouver, ISO, and other styles

43

Yang, X. M. "On E-Convex Sets, E-Convex Functions, and E-Convex Programming." Journal of Optimization Theory and Applications 109, no. 3 (June 2001): 699–704. http://dx.doi.org/10.1023/a:1017532225395.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

Dahiya, Kalpana, Surjeet Kaur Suneja, and Vanita Verma. "Convex programming with single separable constraint and bounded variables." Computational Optimization and Applications 36, no. 1 (November 21, 2006): 67–82. http://dx.doi.org/10.1007/s10589-006-0396-4.

Full text

APA, Harvard, Vancouver, ISO, and other styles

45

Lin, Ming-Hua, Jung-Fa Tsai, Nian-Ze Hu, and Shu-Chuan Chang. "Design Optimization of a Speed Reducer Using Deterministic Techniques." Mathematical Problems in Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/419043.

Full text

Abstract:

The optimal design problem of minimizing the total weight of a speed reducer under constraints is a generalized geometric programming problem. Since the metaheuristic approaches cannot guarantee to find the global optimum of a generalized geometric programming problem, this paper applies an efficient deterministic approach to globally solve speed reducer design problems. The original problem is converted by variable transformations and piecewise linearization techniques. The reformulated problem is a convex mixed-integer nonlinear programming problem solvable to reach an approximate global solution within an acceptable error. Experiment results from solving a practical speed reducer design problem indicate that this study obtains a better solution comparing with the other existing methods.

APA, Harvard, Vancouver, ISO, and other styles

46

Virgili-Llop, Josep, Costantinos Zagaris, Richard Zappulla, Andrew Bradstreet, and Marcello Romano. "A convex-programming-based guidance algorithm to capture a tumbling object on orbit using a spacecraft equipped with a robotic manipulator." International Journal of Robotics Research 38, no. 1 (December 10, 2018): 40–72. http://dx.doi.org/10.1177/0278364918804660.

Full text

Abstract:

An algorithm to guide the capture of a tumbling resident space object by a spacecraft equipped with a robotic manipulator is presented. A solution to the guidance problem is found by solving a collection of convex programming problems. As convex programming offers deterministic convergence properties, this algorithm is suitable for onboard implementation and real-time use. A set of hardware-in-the-loop experiments substantiates this claim. To cast the guidance problem as a collection of convex programming problems, the capture maneuver is divided into two simultaneously occurring sub-maneuvers: a system-wide translation and an internal re-configuration. These two sub-maneuvers are optimized in two consecutive steps. A sequential convex programming procedure, overcoming the presence of non-convex constraints and nonlinear dynamics, is used on both optimization steps. A proof of convergence is offered for the system-wide translation, while a set of structured heuristics—trust regions—is used for the optimization of the internal re-configuration sub-maneuver. Videos of the numerically simulated and experimentally demonstrated maneuvers are included as supplementary material.

APA, Harvard, Vancouver, ISO, and other styles

47

Gil-González, Walter, Alexander Molina-Cabrera, Oscar Danilo Montoya, and Luis Fernando Grisales-Noreña. "An MI-SDP Model for Optimal Location and Sizing of Distributed Generators in DC Grids That Guarantees the Global Optimum." Applied Sciences 10, no. 21 (October 30, 2020): 7681. http://dx.doi.org/10.3390/app10217681.

Full text

Abstract:

This paper deals with a classical problem in power system analysis regarding the optimal location and sizing of distributed generators (DGs) in direct current (DC) distribution networks using the mathematical optimization. This optimization problem is divided into two sub-problems as follows: the optimal location of DGs is a problem, with those with a binary structure being the first sub-problem; and the optimal sizing of DGs with a nonlinear programming (NLP) structure is the second sub-problem. These problems originate from a general mixed-integer nonlinear programming model (MINLP), which corresponds to an NP-hard optimization problem. It is not possible to provide the global optimum with conventional programming methods. A mixed-integer semidefinite programming (MI-SDP) model is proposed to address this problem, where the binary part is solved via the branch and bound (B&B) methods and the NLP part is solved via convex optimization (i.e., SDP). The main advantage of the proposed MI-SDP model is the possibility of guaranteeing a global optimum solution if each of the nodes in the B&B search is convex, as is ensured by the SDP method. Numerical validations in two test feeders composed of 21 and 69 nodes demonstrate that in all of these problems, the optimal global solution is reached by the MI-SDP approach, compared to the classical metaheuristic and hybrid programming models reported in the literature. All the simulations have been carried out using the MATLAB software with the CVX tool and the Mosek solver.

APA, Harvard, Vancouver, ISO, and other styles

48

Hauser, Kris. "Semi-infinite programming for trajectory optimization with non-convex obstacles." International Journal of Robotics Research 40, no. 10-11 (January 10, 2021): 1106–22. http://dx.doi.org/10.1177/0278364920983353.

Full text

Abstract:

This article presents a novel optimization method that handles collision constraints with complex, non-convex 3D geometries. The optimization problem is cast as a semi-infinite program in which each collision constraint is implicitly treated as an infinite number of numeric constraints. The approach progressively generates some of these constraints for inclusion in a finite nonlinear program. Constraint generation uses an oracle to detect points of deepest penetration, and this oracle is implemented efficiently via signed distance field (SDF) versus point cloud collision detection. This approach is applied to pose optimization and trajectory optimization for both free-flying rigid bodies and articulated robots. Experiments demonstrate performance improvements compared with optimizers that handle only convex polyhedra, and demonstrate efficient collision avoidance between non-convex CAD models and point clouds in a variety of pose and trajectory optimization settings.

APA, Harvard, Vancouver, ISO, and other styles

49

Hassan, Mansur, and Adam Baharum. "Modified Courant-Beltrami penalty function and a duality gap for invex optimization problem." International Journal for Simulation and Multidisciplinary Design Optimization 10 (2019): A10. http://dx.doi.org/10.1051/smdo/2019010.

Full text

Abstract:

In this paper, we modified a Courant-Beltrami penalty function method for constrained optimization problem to study a duality for convex nonlinear mathematical programming problems. Karush-Kuhn-Tucker (KKT) optimality conditions for the penalized problem has been used to derived KKT multiplier based on the imposed additional hypotheses on the constraint function g. A zero-duality gap between an optimization problem constituted by invex functions with respect to the same function η and their Lagrangian dual problems has also been established. The examples have been provided to illustrate and proved the result for the broader class of convex functions, termed invex functions.

APA, Harvard, Vancouver, ISO, and other styles

50

Shen, Feichao, Ying Zhang, and Xueyong Wang. "An Accelerated Proximal Algorithm for the Difference of Convex Programming." Mathematical Problems in Engineering 2021 (April 24, 2021): 1–9. http://dx.doi.org/10.1155/2021/9994015.

Full text

Abstract:

In this paper, we propose an accelerated proximal point algorithm for the difference of convex (DC) optimization problem by combining the extrapolation technique with the proximal difference of convex algorithm. By making full use of the special structure of DC decomposition and the information of stepsize, we prove that the proposed algorithm converges at rate of O 1 / k 2 under milder conditions. The given numerical experiments show the superiority of the proposed algorithm to some existing algorithms.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!