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Journal articles on the topic 'Semidefinite programming'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Helmberg, C. "Semidefinite programming." European Journal of Operational Research 137, no. 3 (2002): 461–82. http://dx.doi.org/10.1016/s0377-2217(01)00143-6.

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2

Vandenberghe, Lieven, and Stephen Boyd. "Semidefinite Programming." SIAM Review 38, no. 1 (1996): 49–95. http://dx.doi.org/10.1137/1038003.

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3

Overton, Michael, and Henry Wolkowicz. "Semidefinite programming." Mathematical Programming 77, no. 1 (1997): 105–9. http://dx.doi.org/10.1007/bf02614431.

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4

Yurtsever, Alp, Joel A. Tropp, Olivier Fercoq, Madeleine Udell, and Volkan Cevher. "Scalable Semidefinite Programming." SIAM Journal on Mathematics of Data Science 3, no. 1 (2021): 171–200. http://dx.doi.org/10.1137/19m1305045.

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5

Vandenberghe, Lieven, and Stephen Boyd. "Applications of semidefinite programming." Applied Numerical Mathematics 29, no. 3 (1999): 283–99. http://dx.doi.org/10.1016/s0168-9274(98)00098-1.

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6

Goldfarb, D., and K. Scheinberg. "On parametric semidefinite programming." Applied Numerical Mathematics 29, no. 3 (1999): 361–77. http://dx.doi.org/10.1016/s0168-9274(98)00102-0.

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7

Yang, Hongli, Chengdan Wang, Xiao Bi, and Ivan Ganchev Ivanov. "Robust Invariance Conditions of Uncertain Linear Discrete Time Systems Based on Semidefinite Programming Duality." Mathematics 12, no. 16 (2024): 2512. http://dx.doi.org/10.3390/math12162512.

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This article proposes a novel robust invariance condition for uncertain linear discrete-time systems with state and control constraints, utilizing a method of semidefinite programming duality. The approach involves approximating the robust invariant set for these systems by tackling the dual problem associated with semidefinite programming. Central to this method is the formulation of a dual programming through the application of adjoint mapping. From the standpoint of semidefinite programming dual optimization, the paper presents a novel linear matrix inequality (LMI) conditions pertinent to

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8

Kalantari, Bahman. "Semidefinite programming and matrix scaling over the semidefinite cone." Linear Algebra and its Applications 375 (December 2003): 221–43. http://dx.doi.org/10.1016/s0024-3795(03)00664-5.

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9

Lidický, Bernard, and Florian Pfender. "Semidefinite Programming and Ramsey Numbers." SIAM Journal on Discrete Mathematics 35, no. 4 (2021): 2328–44. http://dx.doi.org/10.1137/18m1169473.

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10

Bofill, Walter Gómez, and Juan A. Gómez. "LINEAR AND NONLINEAR SEMIDEFINITE PROGRAMMING." Pesquisa Operacional 34, no. 3 (2014): 495–520. http://dx.doi.org/10.1590/0101-7438.2014.034.03.0495.

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11

Zhang, Tianyu, and Liwei Zhang. "Critical Multipliers in Semidefinite Programming." Asia-Pacific Journal of Operational Research 37, no. 04 (2020): 2040012. http://dx.doi.org/10.1142/s0217595920400126.

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It was proved in Izmailov and Solodov (2014). Newton-Type Methods for Optimization and Variational Problems, Springer] that the existence of a noncritical multiplier for a (smooth) nonlinear programming problem is equivalent to an error bound condition for the Karush–Kuhn–Thcker (KKT) system without any assumptions. This paper investigates whether this result still holds true for a (smooth) nonlinear semidefinite programming (SDP) problem. The answer is negative: the existence of noncritical multiplier does not imply the error bound condition for the KKT system without additional conditions, w

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12

d’Aspremont, Alexandre. "Subsampling Algorithms for Semidefinite Programming." Stochastic Systems 1, no. 2 (2011): 274–305. http://dx.doi.org/10.1287/10-ssy018.

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13

Zhang, Qinghong, Gang Chen, and Ting Zhang. "Duality formulations in semidefinite programming." Journal of Industrial & Management Optimization 6, no. 4 (2010): 881–93. http://dx.doi.org/10.3934/jimo.2010.6.881.

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14

Schellewald, C., and C. Schnörr. "Subgraph Matching with Semidefinite Programming." Electronic Notes in Discrete Mathematics 12 (March 2003): 279–89. http://dx.doi.org/10.1016/s1571-0653(04)00493-7.

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15

Malick, Jérôme, Janez Povh, Franz Rendl, and Angelika Wiegele. "Regularization Methods for Semidefinite Programming." SIAM Journal on Optimization 20, no. 1 (2009): 336–56. http://dx.doi.org/10.1137/070704575.

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16

Penot, Jean-Paul. "Optimality Conditions in Semidefinite Programming." Numerical Functional Analysis and Optimization 35, no. 7-9 (2014): 1174–96. http://dx.doi.org/10.1080/01630563.2014.895763.

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17

Rendl, Franz. "Semidefinite programming and combinatorial optimization." Applied Numerical Mathematics 29, no. 3 (1999): 255–81. http://dx.doi.org/10.1016/s0168-9274(98)00097-x.

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18

Thake, A. J., P. J. McLellan, and J. F. Forbes. "Controller Approximation Using Semidefinite Programming." Industrial & Engineering Chemistry Research 38, no. 7 (1999): 2699–708. http://dx.doi.org/10.1021/ie980536h.

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19

Yuan, Ganzhao, Zhenjie Zhang, Bernard Ghanem, and Zhifeng Hao. "Low-rank quadratic semidefinite programming." Neurocomputing 106 (April 2013): 51–60. http://dx.doi.org/10.1016/j.neucom.2012.10.014.

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20

Shapiro, Alexander. "Statistical inference of semidefinite programming." Mathematical Programming 174, no. 1-2 (2018): 77–97. http://dx.doi.org/10.1007/s10107-018-1250-z.

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21

Bogaerts, Mathieu, and Peter Dukes. "Semidefinite programming for permutation codes." Discrete Mathematics 326 (July 2014): 34–43. http://dx.doi.org/10.1016/j.disc.2014.03.002.

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22

Ramana, Motakuri V., Levent Tunçel, and Henry Wolkowicz. "Strong Duality for Semidefinite Programming." SIAM Journal on Optimization 7, no. 3 (1997): 641–62. http://dx.doi.org/10.1137/s1052623495288350.

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23

Zhang, Qinghong. "Embedding methods for semidefinite programming." Optimization Methods and Software 27, no. 3 (2012): 461–82. http://dx.doi.org/10.1080/10556788.2010.534475.

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24

Lovász, László. "Integer sequences and semidefinite programming." Publicationes Mathematicae Debrecen 56, no. 3-4 (2000): 475–79. http://dx.doi.org/10.5486/pmd.2000.2362.

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25

Goemans, Michel X. "Semidefinite programming in combinatorial optimization." Mathematical Programming 79, no. 1-3 (1997): 143–61. http://dx.doi.org/10.1007/bf02614315.

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26

Zhao, Qi, and Zhongwen Chen. "An SQP-type Method with Superlinear Convergence for Nonlinear Semidefinite Programming." Asia-Pacific Journal of Operational Research 35, no. 03 (2018): 1850009. http://dx.doi.org/10.1142/s0217595918500094.

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A sequentially semidefinite programming method is proposed for solving nonlinear semidefinite programming problem (NLSDP). Inspired by the sequentially quadratic programming (SQP) method, the algorithm generates a search direction by solving a quadratic semidefinite programming subproblem at each iteration. The [Formula: see text] exact penalty function and a line search strategy are used to determine whether the trial step can be accepted or not. Under mild assumptions, the proposed algorithm is globally convergent. In order to avoid the Maratos effect, we present a modified SQP-type algorith

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27

Lasserre, Jean B. "Semidefinite Programming vs. LP Relaxations for Polynomial Programming." Mathematics of Operations Research 27, no. 2 (2002): 347–60. http://dx.doi.org/10.1287/moor.27.2.347.322.

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28

Deák, István, Imre Pólik, András Prékopa, and Tamás Terlaky. "Convex approximations in stochastic programming by semidefinite programming." Annals of Operations Research 200, no. 1 (2011): 171–82. http://dx.doi.org/10.1007/s10479-011-0986-0.

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29

Chen, Yannan, Yuhong Dai, Deren Han, and Wenyu Sun. "Positive Semidefinite Generalized Diffusion Tensor Imaging via Quadratic Semidefinite Programming." SIAM Journal on Imaging Sciences 6, no. 3 (2013): 1531–52. http://dx.doi.org/10.1137/110843526.

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30

Burer, Samuel. "Semidefinite Programming in the Space of Partial Positive Semidefinite Matrices." SIAM Journal on Optimization 14, no. 1 (2003): 139–72. http://dx.doi.org/10.1137/s105262340240851x.

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31

Ding, Ke-wei. "Distributionally Robust Joint Chance Constrained Problem under Moment Uncertainty." Journal of Applied Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/487178.

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We discuss and develop the convex approximation for robust joint chance constraints under uncertainty of first- and second-order moments. Robust chance constraints are approximated by Worst-Case CVaR constraints which can be reformulated by a semidefinite programming. Then the chance constrained problem can be presented as semidefinite programming. We also find that the approximation for robust joint chance constraints has an equivalent individual quadratic approximation form.

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32

Wang, Po-Wei, and J. Zico Kolter. "Low-Rank Semidefinite Programming for the MAX2SAT Problem." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 1641–49. http://dx.doi.org/10.1609/aaai.v33i01.33011641.

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This paper proposes a new algorithm for solving MAX2SAT problems based on combining search methods with semidefinite programming approaches. Semidefinite programming techniques are well-known as a theoretical tool for approximating maximum satisfiability problems, but their application has traditionally been very limited by their speed and randomized nature. Our approach overcomes this difficult by using a recent approach to low-rank semidefinite programming, specialized to work in an incremental fashion suitable for use in an exact search algorithm. The method can be used both within complete

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33

Wu, Jia, Yi Zhang, Liwei Zhang, and Yue Lu. "A Sequential Convex Program Approach to an Inverse Linear Semidefinite Programming Problem." Asia-Pacific Journal of Operational Research 33, no. 04 (2016): 1650025. http://dx.doi.org/10.1142/s0217595916500251.

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This paper is devoted to the study of solving method for a type of inverse linear semidefinite programming problem in which both the objective parameter and the right-hand side parameter of the linear semidefinite programs are required to adjust. Since such kind of inverse problem is equivalent to a mathematical program with semidefinite cone complementarity constraints which is a rather difficult problem, we reformulate it as a nonconvex semi-definte programming problem by introducing a nonsmooth partial penalty function to penalize the complementarity constraint. The penalized problem is act

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34

Vo, Cong, Masakazu Muramatsu, and Masakazu Kojima. "EQUALITY BASED CONTRACTION OF SEMIDEFINITE PROGRAMMING RELAXATIONS IN POLYNOMIAL OPTIMIZATION." Journal of the Operations Research Society of Japan 51, no. 1 (2008): 111–25. http://dx.doi.org/10.15807/jorsj.51.111.

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35

Fushiki, Tadayoshi. "Estimation of Positive Semidefinite Correlation Matrices by Using Convex Quadratic Semidefinite Programming." Neural Computation 21, no. 7 (2009): 2028–48. http://dx.doi.org/10.1162/neco.2009.04-08-765.

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The correlation matrix is a fundamental statistic that used in many fields. For example, GroupLens, a collaborative filtering system, uses the correlation between users for predictive purposes. Since the correlation is a natural similarity measure between users, the correlation matrix may be used as the Gram matrix in kernel methods. However, the estimated correlation matrix sometimes has a serious defect: although the correlation matrix is originally positive semidefinite, the estimated one may not be positive semidefinite when not all ratings are observed. To obtain a positive semidefinite c

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36

Gvozdenović, Nebojša, Monique Laurent, and Frank Vallentin. "Block-diagonal semidefinite programming hierarchies for 0/1 programming." Operations Research Letters 37, no. 1 (2009): 27–31. http://dx.doi.org/10.1016/j.orl.2008.10.003.

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37

Blanco, Victor, Justo Puerto, and Safae El Haj Ben Ali. "A Semidefinite Programming approach for solving Multiobjective Linear Programming." Journal of Global Optimization 58, no. 3 (2013): 465–80. http://dx.doi.org/10.1007/s10898-013-0056-z.

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38

Mu, Xuewen, and Yaling Zhang. "A Rank-Two Feasible Direction Algorithm for the Binary Quadratic Programming." Journal of Applied Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/963563.

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Based on the semidefinite programming relaxation of the binary quadratic programming, a rank-two feasible direction algorithm is presented. The proposed algorithm restricts the rank of matrix variable to be two in the semidefinite programming relaxation and yields a quadratic objective function with simple quadratic constraints. A feasible direction algorithm is used to solve the nonlinear programming. The convergent analysis and time complexity of the method is given. Coupled with randomized algorithm, a suboptimal solution is obtained for the binary quadratic programming. At last, we report

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39

Duarte, Belmiro P. M. "Exact Optimal Designs of Experiments for Factorial Models via Mixed-Integer Semidefinite Programming." Mathematics 11, no. 4 (2023): 854. http://dx.doi.org/10.3390/math11040854.

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The systematic design of exact optimal designs of experiments is typically challenging, as it results in nonconvex optimization problems. The literature on the computation of model-based exact optimal designs of experiments via mathematical programming, when the covariates are categorical variables, is still scarce. We propose mixed-integer semidefinite programming formulations, to find exact D-, A- and I-optimal designs for linear models, and locally optimal designs for nonlinear models when the design domain is a finite set of points. The strategy requires: (i) the generation of a set of can

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40

Fu, Taoran. "On Doubly Positive Semidefinite Programming Relaxations." Journal of Computational Mathematics 36, no. 3 (2018): 391–403. http://dx.doi.org/10.4208/jcm.1708-m2017-0130.

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41

Rontsis, Nikitas, Paul Goulart, and Yuji Nakatsukasa. "Efficient Semidefinite Programming with Approximate ADMM." Journal of Optimization Theory and Applications 192, no. 1 (2021): 292–320. http://dx.doi.org/10.1007/s10957-021-01971-3.

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AbstractTenfold improvements in computation speed can be brought to the alternating direction method of multipliers (ADMM) for Semidefinite Programming with virtually no decrease in robustness and provable convergence simply by projecting approximately to the Semidefinite cone. Instead of computing the projections via “exact” eigendecompositions that scale cubically with the matrix size and cannot be warm-started, we suggest using state-of-the-art factorization-free, approximate eigensolvers, thus achieving almost quadratic scaling and the crucial ability of warm-starting. Using a recent resul

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42

Hauenstein, Jonathan D., Alan C. Liddell, Sanesha McPherson, and Yi Zhang. "Numerical algebraic geometry and semidefinite programming." Results in Applied Mathematics 11 (August 2021): 100166. http://dx.doi.org/10.1016/j.rinam.2021.100166.

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43

Mullan, Michael, and Emanuel Knill. "Improving quantum clocks via semidefinite programming." Quantum Information and Computation 12, no. 7&8 (2012): 553–74. http://dx.doi.org/10.26421/qic12.7-8-2.

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The accuracies of modern quantum logic clocks have surpassed those of standard atomic fountain clocks. These clocks also provide a greater degree of control, because before and after clock queries, we are able to apply chosen unitary operations and measurements. Here, we take advantage of these choices and present a numerical technique designed to increase the accuracy of these clocks. We use a greedy approach, minimizing the phase variance of a noisy classical oscillator with respect to a perfect frequency standard after an interrogation step; we do not optimize over successive interrogations

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44

Vandenberghe, Lieven, Stephen Boyd, and Katherine Comanor. "Generalized Chebyshev Bounds via Semidefinite Programming." SIAM Review 49, no. 1 (2007): 52–64. http://dx.doi.org/10.1137/s0036144504440543.

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45

Comanor, Katherine, Lieven Vandenberghe, and Stephen Boyd. "SEMIDEFINITE PROGRAMMING AND MULTIVARIATE CHEBYSHEV BOUNDS." IFAC Proceedings Volumes 39, no. 9 (2006): 597–601. http://dx.doi.org/10.3182/20060705-3-fr-2907.00102.

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46

Karger, David, Rajeev Motwani, and Madhu Sudan. "Approximate graph coloring by semidefinite programming." Journal of the ACM 45, no. 2 (1998): 246–65. http://dx.doi.org/10.1145/274787.274791.

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47

Li, Hongying, Marc C. Robini, Feng Yang, Isabelle Magnin, and Yuemin Zhu. "Cardiac Fiber Unfolding by Semidefinite Programming." IEEE Transactions on Biomedical Engineering 62, no. 2 (2015): 582–92. http://dx.doi.org/10.1109/tbme.2014.2360797.

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48

Zhang, Shuzhong, and Yongwei Huang. "Complex Quadratic Optimization and Semidefinite Programming." SIAM Journal on Optimization 16, no. 3 (2006): 871–90. http://dx.doi.org/10.1137/04061341x.

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49

Musin, O. R. "Bounds for codes by semidefinite programming." Proceedings of the Steklov Institute of Mathematics 263, no. 1 (2008): 134–49. http://dx.doi.org/10.1134/s0081543808040111.

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50

Yang, Shouhong. "Semidefinite programming via image space analysis." Journal of Industrial and Management Optimization 12, no. 4 (2016): 1187–97. http://dx.doi.org/10.3934/jimo.2016.12.1187.

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