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Operations Research Transactions >

2021 , Vol. 25 >Issue 4: 69 - 79

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2021.04.006

Projected Levenberg-Marquardt method for stochastic R0 tensor complementarity problems

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  • 1. School of Mathematics and Statistics, Qingdao University, Qingdao 266071, Shandong, China

Received date: 2019-10-29

  Online published: 2021-12-11

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Abstract

In this paper, we consider a class of stochastic R0 tensor complementarity problems with finitely many elements. Firstly, we use Fischer-Burmeister function to transform the problem into a constrained optimization problem. Then a projected Levenberg-Marquardt method is used to solve the constrained optimization problem. Under general conditions, the global convergence of this method is proved, and the related numerical results show the efficiency of the method.

Key words： stochastic R0 tensor complementarity problem; projected Levenberg-Marquardt method; global convergence; line search

Cite this article

Liyuan CUI, Shouqiang DU . Projected Levenberg-Marquardt method for stochastic R0 tensor complementarity problems[J]. Operations Research Transactions, 2021 , 25(4) : 69 -79 . DOI: 10.15960/j.cnki.issn.1007-6093.2021.04.006

References

1 Che M L , Qi L Q , Wei Y M . Stochastic $R_0$ tensors to stochastic tensor complementarity problems[J]. Optimization Letters, 2019, 13, 261- 279.
2 Song Y S , Qi L Q . Properties of tensor complementarity problem and some classes of structured tensors[J]. Annals of Applied Mathematics, 2017, 33, 308- 323.
3 Song Y S , Yu G H . Properties of solution set of tensor complementarity problem[J]. Journal of Optimization Theory and Applications, 2016, 170, 85- 96.
4 Song Y S , Qi L Q . Tensor complementarity problem and semi-positive tensors[J]. Journal of Optimization Theory and Applications, 2016, 169 (3): 1069- 1078.
5 Ding W Y , Luo Z Y , Qi L Q . $P$-tensors, $P_0$-tensors, and their applications[J]. Linear Algebra Applications, 2018, 555, 336- 354.
6 Huang Z H , Qi L Q . Formulating an $n$-person noncooperative game as a tensor complementarity problem[J]. Computational Optimization and Applications, 2017, 66 (3): 557- 576.
7 Bai X L , Hang Z H , Wang Y . Global uniqueness and solvability for tensor complementarity problems[J]. Journal of Optimization Theory and Applications, 2016, 170 (1): 72- 84.
8 Du S Q , Zhang L P . A mixed integer programming approach to the tensor complementarity problem[J]. Journal of Global Optimization, 2019, 73, 789- 800.
9 李浙宁, 凌晨, 王宜举, 等. 张量分析和多项式优化的若干进展[J]. 运筹学学报, 2014, 18 (1): 134- 148.
10 徐凤, 凌晨. 高阶张量Pareto-特征值的若干性质[J]. 运筹学学报, 2015, 19 (3): 34- 41.
11 Zhou G L , Caccetta L . Feasible semismooth Newton method for a class of stochastic linear complementarity problems[J]. Journal of Optimization Theory and Applications, 2008, 139, 379- 392.
12 Liu H W , Huang Y K , Li X L . New reformulation and feasible semismooth Newton method for a class of stochastic linear complementarity problems[J]. Applied Mathematics and Computation, 2011, 217 (23): 9723- 9740.
13 Chen X J , Fukushima M . Expected residual minimization method for stochastic linear complementary problems[J]. Mathematics of Operations Research, 2005, 30 (4): 1022- 1038.
14 Gurkan G , Yoncaozgea Y , Robinson S M . Sample-path solution of stochastic variational inequalities[J]. Mathematical Programming, 1994, 84 (2): 313- 333.
15 Fischer A . A special Newton-type optimization method[J]. Optimization, 1992, 24, 269- 284.
16 Facchinei F , Pang J H . Finite-dimensional variational inequalities and complementarity problem[M]. New York: Springer, 2003.
17 Qi L Q , Sun J . A nonsmooth version of Newton's method[J]. Mathematical Programming, 1993, 58, 353- 367.
18 Sun D F , Qi L Q . On NCP-Functions[J]. Computational Optimization and Applications, 1999, 13, 201- 220.
19 Kanzow C . An unconstrained optimization technique for large-scale linearly constrained convex minimization problems[J]. Computing, 1994, 53 (2): 101- 117.
20 Kanzow C . Global convergence properties of some iterative methods for linear complementarity problems[J]. SIAM Journal on Optimization, 1996, 6 (2): 326- 341.
21 周莎. 离散型随机线性互补问题算法的研究[D]. 桂林: 桂林电子科技大学, 2014.
22 Chen B T , Chen X J , Kanzow C . A penalized Fischer-Burmeister NCP-function[J]. Mathematical Programming, 2000, 88 (1): 211- 216.
23 Birgin E G , Martinez J M , Raydan M . Nonmonotone spectral projected gradient methods on convex sets[J]. SIAM Journal on Optimization, 2000, 10, 196- 211.
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