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

Abstract

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.