Class Of Stochastic Complementarity Problems Research Articles

Infeasible interior-point algorithms based on sampling average approximations for a class of stochastic complementarity problems and their applications

This paper considers a class of stochastic complementarity problems (SCP). Different from the classical complementarity problems, the SCP contains a mathematical expectation, which may not be evaluated in an explicit form in general. We combine an interior-point algorithm for deterministic cases with the well-known sample average approximation (SAA) techniques to present an SAA-based infeasible interior-point algorithm for the SCP. We investigate the convergence properties and computational complexity of the proposed algorithm under mild assumptions. Then, we extend these results to a class of mixed SCPs. Furthermore, we apply the proposed algorithms to solve a stochastic natural gas transmission problem and a stochastic oligopoly model. Preliminary numerical experiments indicate that the proposed approach is competitive with some existing methods. • We study a class of stochastic complementarity problems. • We present an infeasible interior-point algorithm for the considered problem. • We investigate convergence properties and computational complexity of the algorithm. • We apply the proposed approach to natural gas transmission and oligopoly problems.

Properties of Expected Residual Minimization Model for a Class of Stochastic Complementarity Problems

Expected residual minimization (ERM) model which minimizes an expected residual function defined by an NCP function has been studied in the literature for solving stochastic complementarity problems. In this paper, we first give the definitions of stochasticP-function, stochasticP0-function, and stochastic uniformlyP-function. Furthermore, the conditions such that the function is a stochasticPP0-function are considered. We then study the boundedness of solution set and global error bounds of the expected residual functions defined by the “Fischer-Burmeister” (FB) function and “min” function. The conclusion indicates that solutions of the ERM model are robust in the sense that they may have a minimum sensitivity with respect to random parameter variations in stochastic complementarity problems. On the other hand, we employ quasi-Monte Carlo methods and derivative-free methods to solve ERM model.