Robust solution of monotone stochastic linear complementarity problems

被引:15
|
作者
Xiaojun Chen
Chao Zhang
Masao Fukushima
机构
[1] Hirosaki University,Department of Mathematical Sciences, Faculty of Science and Technology
[2] Kyoto University,Department of Applied Mathematics and Physics, Graduate School of Informatics
来源
Mathematical Programming | 2009年 / 117卷
关键词
Stochastic linear complementarity problem; NCP function; Expected residual minimization; 90C15; 90C33;
D O I
暂无
中图分类号
学科分类号
摘要
We consider the stochastic linear complementarity problem (SLCP) involving a random matrix whose expectation matrix is positive semi-definite. We show that the expected residual minimization (ERM) formulation of this problem has a nonempty and bounded solution set if the expected value (EV) formulation, which reduces to the LCP with the positive semi-definite expectation matrix, has a nonempty and bounded solution set. We give a new error bound for the monotone LCP and use it to show that solutions of the ERM formulation are robust in the sense that they may have a minimum sensitivity with respect to random parameter variations in SLCP. Numerical examples including a stochastic traffic equilibrium problem are given to illustrate the characteristics of the solutions.
引用
收藏
页码:51 / 80
页数:29
相关论文
共 50 条
  • [31] A Polynomial Interior-Point Algorithm for Monotone Linear Complementarity Problems
    Mansouri, H.
    Pirhaji, M.
    JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2013, 157 (02) : 451 - 461
  • [32] A Polynomial Interior-Point Algorithm for Monotone Linear Complementarity Problems
    H. Mansouri
    M. Pirhaji
    Journal of Optimization Theory and Applications, 2013, 157 : 451 - 461
  • [33] The largest step path following algorithm for monotone linear complementarity problems
    Department of Mathematics, Federal University of Santa Catarina, Cx. Postal 5210, 88040 Florianopolis, SC, Brazil
    Math Program Ser B, 2 (309-332):
  • [34] On the solution of linear complementarity problem by a stochastic iteration method
    Okoroafor, A. Alfred
    Osu, Bright O.
    Journal of Applied Sciences, 2006, 6 (12) : 2685 - 2687
  • [35] ON ROBUST SOLUTIONS TO UNCERTAIN LINEAR COMPLEMENTARITY PROBLEMS AND THEIR VARIANTS
    Xie, Yue
    Shanbhag, Uday V.
    SIAM JOURNAL ON OPTIMIZATION, 2016, 26 (04) : 2120 - 2159
  • [36] Γ-robust linear complementarity problems with ellipsoidal uncertainty sets
    Krebs, Vanessa
    Mueller, Michael
    Schmidt, Martin
    INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, 2022, 29 (01) : 417 - 441
  • [37] Solvability of monotone tensor complementarity problems
    Liping Zhang
    Defeng Sun
    Zhenting Luan
    Science China Mathematics, 2023, 66 : 647 - 664
  • [38] AN ENUMERATIVE METHOD FOR THE SOLUTION OF LINEAR COMPLEMENTARITY-PROBLEMS
    JUDICE, JJ
    MITRA, G
    EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 1988, 36 (01) : 122 - 128
  • [39] On the solution of NP-hard linear complementarity problems
    Joaquim J. Júdice
    Ana M. Faustino
    Isabel Martins Ribeiro
    Top, 2002, 10 (1) : 125 - 145
  • [40] Solvability of monotone tensor complementarity problems
    Liping Zhang
    Defeng Sun
    Zhenting Luan
    ScienceChina(Mathematics), 2023, 66 (03) : 647 - 664