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Relevant bibliographies by topics / Second-Order Cone Programming / Journal articles

Journal articles on the topic 'Second-Order Cone Programming'

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Author: Grafiati

Published: 4 June 2021

Last updated: 26 January 2023

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1

Alizadeh, F., and D. Goldfarb. "Second-order cone programming." Mathematical Programming 95, no. 1 (January 1, 2003): 3–51. http://dx.doi.org/10.1007/s10107-002-0339-5.

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2

Kobayashi, Kazuhiro, Sunyoung Kim, and Masakazu Kojima. "SPARSE SECOND ORDER CONE PROGRAMMING FORMULATIONS FOR CONVEX OPTIMIZATION PROBLEMS." Journal of the Operations Research Society of Japan 51, no. 3 (2008): 241–64. http://dx.doi.org/10.15807/jorsj.51.241.

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3

Hang, Nguyen T. V., Boris S. Mordukhovich, and M. Ebrahim Sarabi. "Second-order variational analysis in second-order cone programming." Mathematical Programming 180, no. 1-2 (November 3, 2018): 75–116. http://dx.doi.org/10.1007/s10107-018-1345-6.

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4

Xia, Yu. "Two-dimensional Second-Order Cone Programming." International Journal of Operational Research 5, no. 4 (2009): 468. http://dx.doi.org/10.1504/ijor.2009.025704.

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5

Lobo, Miguel Sousa, Lieven Vandenberghe, Stephen Boyd, and Hervé Lebret. "Applications of second-order cone programming." Linear Algebra and its Applications 284, no. 1-3 (November 1998): 193–228. http://dx.doi.org/10.1016/s0024-3795(98)10032-0.

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6

Averbakh, I., and Y. B. Zhao. "Relaxed robust second-order-cone programming." Applied Mathematics and Computation 210, no. 2 (April 2009): 387–97. http://dx.doi.org/10.1016/j.amc.2009.01.019.

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7

Wang, Jiani, and Liwei Zhang. "Statistical Inference of Second-Order Cone Programming." Asia-Pacific Journal of Operational Research 35, no. 06 (December 2018): 1850044. http://dx.doi.org/10.1142/s0217595918500446.

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The randomness of the second-order cone programming problems is mainly reflected in the objective function and the constraints both having random vectors. In this paper, we discuss the statistical properties of estimates of the respective optimal value and optimal solutions when the random vectors are estimated by their sample both in the objective function and the constraints, which are based on perturbation analysis theory of second-order cone programming. As an example we consider the problem of minimizing a sum of norms with weights.

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8

Zhang, Liwei, Shengzhe Gao, and Saoyan Guo. "Statistical Inference of Second-Order Cone Programming." Asia-Pacific Journal of Operational Research 36, no. 02 (April 2019): 1940003. http://dx.doi.org/10.1142/s0217595919400037.

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In this paper, we study the stability of stochastic second-order programming when the probability measure is perturbed. Under the Lipschitz continuity of the objective function and metric regularity of the feasible set-valued mapping, the outer semicontinuity of the optimal solution set and Lipschitz continuity of optimal values are demonstrated. Moreover, we prove that, if the constraint non-degeneracy condition and strong second-order sufficient condition hold at a local minimum point of the original problem, there exists a Lipschitz continuous solution path satisfying the Karush–Kuhn–Tucker conditions.

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9

Liang, Zhizheng. "Feature Scaling via Second-Order Cone Programming." Mathematical Problems in Engineering 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/7347986.

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Feature scaling has attracted considerable attention during the past several decades because of its important role in feature selection. In this paper, a novel algorithm for learning scaling factors of features is proposed. It first assigns a nonnegative scaling factor to each feature of data and then adopts a generalized performance measure to learn the optimal scaling factors. It is of interest to note that the proposed model can be transformed into a convex optimization problem: second-order cone programming (SOCP). Thus the scaling factors of features in our method are globally optimal in some sense. Several experiments on simulated data, UCI data sets, and the gene data set are conducted to demonstrate that the proposed method is more effective than previous methods.

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10

Alzalg, Baha M. "Stochastic second-order cone programming: Applications models." Applied Mathematical Modelling 36, no. 10 (October 2012): 5122–34. http://dx.doi.org/10.1016/j.apm.2011.12.053.

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11

Lourenço, Bruno F., Masakazu Muramatsu, and Takashi Tsuchiya. "Weak infeasibility in second order cone programming." Optimization Letters 10, no. 8 (December 24, 2015): 1743–55. http://dx.doi.org/10.1007/s11590-015-0982-4.

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12

Xia, Yu, and Farid Alizadeh. "The method for second order cone programming." Computers & Operations Research 35, no. 5 (May 2008): 1510–38. http://dx.doi.org/10.1016/j.cor.2006.08.009.

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13

Liu, Xinfu, Zuojun Shen, and Ping Lu. "Entry Trajectory Optimization by Second-Order Cone Programming." Journal of Guidance, Control, and Dynamics 39, no. 2 (February 2016): 227–41. http://dx.doi.org/10.2514/1.g001210.

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14

Bonnans, J. Frédéric, and Héctor Ramírez C. "Perturbation analysis of second-order cone programming problems." Mathematical Programming 104, no. 2-3 (July 14, 2005): 205–27. http://dx.doi.org/10.1007/s10107-005-0613-4.

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15

Pesavento, M., A. B. Gershman, and Zhi-Quan Luo. "Robust array interpolation using second-order cone programming." IEEE Signal Processing Letters 9, no. 1 (January 2002): 8–11. http://dx.doi.org/10.1109/97.988716.

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16

Tsang, I. W., and J. T. Kwok. "Efficient Hyperkernel Learning Using Second-Order Cone Programming." IEEE Transactions on Neural Networks 17, no. 1 (January 2006): 48–58. http://dx.doi.org/10.1109/tnn.2005.860848.

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17

Alhadi, Mohammad Alabed, and Baha Alzalg. "Stochastic Second-Order Cone Programming: The Equivalent Convex Program." Applied Mathematics & Information Sciences 12, no. 3 (May 1, 2018): 601–6. http://dx.doi.org/10.18576/amis/120315.

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18

Tseng, Paul. "Second‐Order Cone Programming Relaxation of Sensor Network Localization." SIAM Journal on Optimization 18, no. 1 (January 2007): 156–85. http://dx.doi.org/10.1137/050640308.

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19

López, Julio, and Sebastián Maldonado. "Multi-class second-order cone programming support vector machines." Information Sciences 330 (February 2016): 328–41. http://dx.doi.org/10.1016/j.ins.2015.10.016.

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20

Yang, Xingtong, and Ming Li. "Free isotropic material optimization via second order cone programming." Computer-Aided Design 115 (October 2019): 52–63. http://dx.doi.org/10.1016/j.cad.2019.05.002.

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21

Yang, Li, Bo Yu, and YanXi Li. "A homotopy method for nonlinear second-order cone programming." Numerical Algorithms 68, no. 2 (March 20, 2014): 355–65. http://dx.doi.org/10.1007/s11075-014-9848-6.

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22

Tang, LiPing, Hong Yan, and XinMin Yang. "Second order duality for multiobjective programming with cone constraints." Science China Mathematics 59, no. 7 (May 18, 2016): 1285–306. http://dx.doi.org/10.1007/s11425-016-5147-0.

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23

Sasakawa, Takashi, and Takashi Tsuchiya. "Optimal Magnetic Shield Design with Second-Order Cone Programming." SIAM Journal on Scientific Computing 24, no. 6 (January 2003): 1930–50. http://dx.doi.org/10.1137/s1064827500380350.

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24

Xia, Yong. "Second order cone programming relaxation for quadratic assignment problems." Optimization Methods and Software 23, no. 3 (June 2008): 441–49. http://dx.doi.org/10.1080/10556780701843405.

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25

Zhong, Ping, and Masao Fukushima. "Second-Order Cone Programming Formulations for Robust Multiclass Classification." Neural Computation 19, no. 1 (January 2007): 258–82. http://dx.doi.org/10.1162/neco.2007.19.1.258.

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Multiclass classification is an important and ongoing research subject in machine learning. Current support vector methods for multiclass classification implicitly assume that the parameters in the optimization problems are known exactly. However, in practice, the parameters have perturbations since they are estimated from the training data, which are usually subject to measurement noise. In this article, we propose linear and nonlinear robust formulations for multiclass classification based on the M-SVM method. The preliminary numerical experiments confirm the robustness of the proposed method.

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26

Steidl, G., S. Setzer, B. Popilka, and B. Burgeth. "Restoration of matrix fields by second-order cone programming." Computing 81, no. 2-3 (November 2007): 161–78. http://dx.doi.org/10.1007/s00607-007-0247-x.

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27

Krabbenhoft, K., and A. V. Lyamin. "Computational Cam clay plasticity using second-order cone programming." Computer Methods in Applied Mechanics and Engineering 209-212 (February 2012): 239–49. http://dx.doi.org/10.1016/j.cma.2011.11.006.

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28

Meng, Jingjing, Ping Cao, Jinsong Huang, Hang Lin, Yu Chen, and Rihong Cao. "Second‐order cone programming formulation of discontinuous deformation analysis." International Journal for Numerical Methods in Engineering 118, no. 5 (January 8, 2019): 243–57. http://dx.doi.org/10.1002/nme.6006.

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29

Chua, Chek Beng. "The Primal-Dual Second-Order Cone Approximations Algorithm for Symmetric Cone Programming." Foundations of Computational Mathematics 7, no. 3 (March 23, 2007): 271–302. http://dx.doi.org/10.1007/s10208-004-0149-7.

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30

Dueri, Daniel, Jing Zhang, and Behcet Açikmese. "Automated Custom Code Generation for Embedded, Real-time Second Order Cone Programming." IFAC Proceedings Volumes 47, no. 3 (2014): 1605–12. http://dx.doi.org/10.3182/20140824-6-za-1003.02736.

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31

Xu, Zhijun, and Jing Zhou. "A Global Optimization Algorithm for Solving Linearly Constrained Quadratic Fractional Problems." Mathematics 9, no. 22 (November 22, 2021): 2981. http://dx.doi.org/10.3390/math9222981.

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This paper first proposes a new and enhanced second order cone programming relaxation using the simultaneous matrix diagonalization technique for the linearly constrained quadratic fractional programming problem. The problem has wide applications in statics, economics and signal processing. Thus, fast and effective algorithm is required. The enhanced second order cone programming relaxation improves the relaxation effect and computational efficiency compared to the classical second order cone programming relaxation. Moreover, although the bound quality of the enhanced second order cone programming relaxation is worse than that of the copositive relaxation, the computational efficiency is significantly enhanced. Then we present a global algorithm based on the branch and bound framework. Extensive numerical experiments show that the enhanced second order cone programming relaxation-based branch and bound algorithm globally solves the problem in less computing time than the copositive relaxation approach.

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32

Zhang, Yaling, and Hongwei Liu. "A new projection neural network for linear and convex quadratic second-order cone programming." Journal of Intelligent & Fuzzy Systems 42, no. 4 (March 4, 2022): 2925–37. http://dx.doi.org/10.3233/jifs-210164.

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A new projection neural network approach is presented for the linear and convex quadratic second-order cone programming. In the method, the optimal conditions of the linear and convex second-order cone programming are equivalent to the cone projection equations. A Lyapunov function is given based on the G-norm distance function. Based on the cone projection function, the descent direction of Lyapunov function is used to design the new projection neural network. For the proposed neural network, we give the Lyapunov stability analysis and prove the global convergence. Finally, some numerical examples and two kinds of grasping force optimization problems are used to test the efficiency of the proposed neural network. The simulation results show that the proposed neural network is efficient for solving some linear and convex quadratic second-order cone programming problems. Especially, the proposed neural network can overcome the oscillating trajectory of the exist projection neural network for some linear second-order cone programming examples and the min-max grasping force optimization problem.

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33

MAO, Zhiwei, Kewei YUAN, and Xianmin WANG. "Second-Order Cone Programming Based Joint Design of OFDM Systems." IEICE Transactions on Communications E94-B, no. 2 (2011): 508–14. http://dx.doi.org/10.1587/transcom.e94.b.508.

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34

Sun, Xin, Baihai Zhang, Runqi Chai, Antonios Tsourdos, and Senchun Chai. "UAV trajectory optimization using chance-constrained second-order cone programming." Aerospace Science and Technology 121 (February 2022): 107283. http://dx.doi.org/10.1016/j.ast.2021.107283.

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35

Inaba, Hiroki, Shinji Mizuno, and Kazuhide Nakata. "ROBUST TRACKING ERROR OPTIMIZATION PROBLEMS BY SECOND-ORDER CONE PROGRAMMING." Transactions of the Operations Research Society of Japan 48 (2005): 12–25. http://dx.doi.org/10.15807/torsj.48.12.

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36

Zhixia Yang, and Yingjie Tian. "Second Order Cone Programming Formulations for Handling Data with Perturbation." Journal of Convergence Information Technology 5, no. 9 (November 30, 2010): 267–78. http://dx.doi.org/10.4156/jcit.vol5.issue9.28.

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37

Chi, Xiaoni, and Sanyang Liu. "A non-interior continuation method for second-order cone programming." Optimization 58, no. 8 (November 2009): 965–79. http://dx.doi.org/10.1080/02331930701763421.

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38

董, 丽. "Smoothing Inexact Newton Method for the Second Order Cone Programming." Advances in Applied Mathematics 04, no. 03 (2015): 271–76. http://dx.doi.org/10.12677/aam.2015.43033.

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39

Gupta, S. K., and D. Dangar. "Duality for second-order symmetric multiobjective programming with cone constraints." International Journal of Mathematics in Operational Research 4, no. 2 (2012): 128. http://dx.doi.org/10.1504/ijmor.2012.046374.

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40

López, Julio, and Sebastián Maldonado. "Robust twin support vector regression via second-order cone programming." Knowledge-Based Systems 152 (July 2018): 83–93. http://dx.doi.org/10.1016/j.knosys.2018.04.005.

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41

Huang, Gao, Shiji Song, Jatinder N. D. Gupta, and Cheng Wu. "A second order cone programming approach for semi-supervised learning." Pattern Recognition 46, no. 12 (December 2013): 3548–58. http://dx.doi.org/10.1016/j.patcog.2013.06.016.

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42

Dorsey, William Mark, Jeffrey O. Coleman, and William R. Pickles. "Uniform circular array pattern synthesis using second‐order cone programming." IET Microwaves, Antennas & Propagation 9, no. 8 (June 2015): 723–27. http://dx.doi.org/10.1049/iet-map.2014.0418.

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43

Maldonado, Sebastián, and Julio López. "Ellipsoidal support vector regression based on second-order cone programming." Neurocomputing 305 (August 2018): 59–69. http://dx.doi.org/10.1016/j.neucom.2018.04.035.

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44

López, Julio, Sebastián Maldonado, and Miguel Carrasco. "Robust nonparallel support vector machines via second-order cone programming." Neurocomputing 364 (October 2019): 227–38. http://dx.doi.org/10.1016/j.neucom.2019.07.072.

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45

Maggioni, F., F. A. Potra, M. I. Bertocchi, and E. Allevi. "Stochastic Second-Order Cone Programming in Mobile Ad Hoc Networks." Journal of Optimization Theory and Applications 143, no. 2 (May 14, 2009): 309–28. http://dx.doi.org/10.1007/s10957-009-9561-0.

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46

Maldonado, Sebastián, and Julio López. "Alternative second-order cone programming formulations for support vector classification." Information Sciences 268 (June 2014): 328–41. http://dx.doi.org/10.1016/j.ins.2014.01.041.

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47

Meng, Jingjing, Xue Zhang, Jinsong Huang, Hongxiang Tang, Hans Mattsson, and Jan Laue. "A smoothed finite element method using second-order cone programming." Computers and Geotechnics 123 (July 2020): 103547. http://dx.doi.org/10.1016/j.compgeo.2020.103547.

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48

Mu, Xuewen, and Yaling Zhang. "A Second-Order Cone Programming Method for Multiuser Detection Problem." Wireless Personal Communications 60, no. 2 (March 17, 2010): 335–44. http://dx.doi.org/10.1007/s11277-010-9947-1.

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49

Kim, Sunyonga, and Masakazu Kojima. "Second order cone programming relaxation of nonconvex quadratic optimization problems." Optimization Methods and Software 15, no. 3-4 (January 2001): 201–24. http://dx.doi.org/10.1080/10556780108805819.

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50

Kim, Sunyoung, Masakazu Kojima, and Makoto Yamashita. "Second Order Cone Programming Relaxation of a Positive Semidefinite Constraint." Optimization Methods and Software 18, no. 5 (October 2003): 535–41. http://dx.doi.org/10.1080/1055678031000148696.

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