FULL LENGTH PAPER

Mathematical Programming

, Volume 117, Issue 1, pp 51-80

First online:

Robust solution of monotone stochastic linear complementarity problems

  • Xiaojun ChenAffiliated withDepartment of Mathematical Sciences, Faculty of Science and Technology, Hirosaki University
  • , Chao ZhangAffiliated withDepartment of Mathematical Sciences, Faculty of Science and Technology, Hirosaki University
  • , Masao FukushimaAffiliated withDepartment of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University Email author 

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Abstract

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.

Keywords

Stochastic linear complementarity problem NCP function Expected residual minimization

Mathematics Subject Classification (2000)

90C15 90C33