Robust solution of monotone stochastic linear complementarity problems
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.
KeywordsStochastic linear complementarity problem NCP function Expected residual minimization
Mathematics Subject Classification (2000)90C15 90C33
Unable to display preview. Download preview PDF.
- 6.Facchinei F. and Pang J.-S. (2003). Finite-Dimensional Variational Inequalities and Complementarity Problems, I and II. Springer, New York Google Scholar
- 7.Fang, H., Chen, X., Fukushima, M.: Stochastic R 0 matrix linear complementarity problems. SIAM J. Optim. 18, 482–506 (2007)Google Scholar
- 8.Ferris, M.C.: ftp://ftp.cs.wisc.edu/math-prog/matlab/lemke.m, Department of Computer Science, University of Wisconsin (1998)Google Scholar
- 16.Luo Z.-Q. and Tseng P. (1997). A new class of merit functions for the nonlinear complementarity problem. In: Ferris, M.C. and Pang, J.-S. (eds) Complementarity and Variational Problems: State of the Art., pp 204–225. SIAM, Philadelphia Google Scholar