A sample average approximation regularization method for a stochastic mathematical program with general vertical complementarity constraints

Indexed by:Journal Papers

Journal:JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Included Journals:SCIE、EI、Scopus

Volume:280

Issue:1

Page Number:202-216

ISSN No.:0377-0427

Key Words:Sample average approximation; Log-exponential function; Stochastic mathematical program with general vertical complementarity constraints; Stochastic Stackelberg game

Abstract:Based on the log-exponential function, a sample average approximation (SAA) regularization method is proposed for solving a stochastic mathematical program with general vertical complementarity constraints (SMPVCC) considered by Birbil et al. (2006). Detailed convergence analysis of this method is investigated. It is demonstrated that under some regularity conditions, any accumulation point of the sequence of optimal solutions of SAA regularized problem is almost surely an optimal solution of the SMPVCC as the parameter tends to zero and the sample size tends to infinity. Furthermore, the optimal value sequence of SPA regularized problem converges to the optimal value of SMPVCC with exponential convergence rate with probability one and a sequence of stationary points of regularized SAA problem converges almost surely to a stationary point of SMPVCC. Finally, we show that a stochastic Stackelberg game can be formulated as a SMPVCC problem and an equilibrium solution can be obtained by the method proposed. (C) 2014 Elsevier B.V. All rights reserved.

Date of Publication:2015-05-15