随机二阶锥二次规划逆问题的SAA方法

doi:10.15960/j.cnki.issn.1007-6093.2022.02.003

Operations Research Transactions ›› 2022, Vol. 26 ›› Issue (2): 31-44.doi: 10.15960/j.cnki.issn.1007-6093.2022.02.003

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An SAA approach for a class of second-order cone stochastic inverse quadratic programming problem

Bo WANG¹, Li CHU²^,*(), Liwei ZHANG³, Hongwei ZHANG³

1. Key Laboratory of Operations Research and Control of Universities in Fujian, School of Mathematics and Statistics, Fuzhou University, Fuzhou 350116, Fujian, China
2. College of Computer Science and Mathematics, Fujian University of Technology, Fuzhou 350118, Fujian, China
3. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, Liaoning, China

Received:2020-06-23 Online:2022-06-15 Published:2022-05-27
Contact: Li CHU E-mail:sophiatruly@126.com

Abstract

Abstract:

In this paper, we consider a class of stochastic inverse quadratic second-order cone programming problem. This stochastic model contains complementarity constraints, and is more proper to model some class of real world problems. By employing the techniques of stochastic sampling and smoothing, we construct auxiliary approximate sub-problems to solve the original model. In addition, we proved that if the solutions of the approximate sub-problems converge, then with probability one the limit is the C-stationary point of the original problem. If strict complementarity condition and the second order necessary condition hold, then with probability one the limit is an M-stationary point. A simple numerical test verified the applicability of our approach.

Key words: stochastic sampling, complementarity constraint, second-order cone programming

CLC Number:

Bo WANG, Li CHU, Liwei ZHANG, Hongwei ZHANG. An SAA approach for a class of second-order cone stochastic inverse quadratic programming problem[J]. Operations Research Transactions, 2022, 26(2): 31-44.

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References

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N	ErrSOC	ErrCom	ErrSol	运行时间/s
50	0	8.10×10^-2	1.96×10^-1	1.01
100	0	8.65×10^-2	2.90×10^-1	1.12
200	0	9.92×10^-2	8.49×10^-2	2.47
500	0	8.63×10^-2	6.51×10^-2	5.60
1 000	0	8.97×10^-2	4.31×10^-2	8.46
5 000	0	8.37×10^-2	1.42×10^-2	73.16
10 000	0	8.39×10^-2	2.10×10^-2	47.11
20 000	0	8.34×10^-2	1.81×10^-2	261.29
50 000	0	8.15×10^-2	8.89×10^-3	110.73

[1]	CHEN Lin, YANG Xinmin. Optimality conditions for a class of stochastic optimization problems with probabilistic complementarity constraints [J]. Operations Research Transactions, 2017, 21(2): 24-30.
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An SAA approach for a class of second-order cone stochastic inverse quadratic programming problem

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