Two-stage stochastic variational inequalities: an ERM-solution procedure

• 成果类型: Article
• 署名作者: Chen, Xiaojun; Pong, Ting Kei; Wets, Roger J-B.
• 署名单位: Hong Kong Polytechnic University; University of California System; University of California Davis
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-017-1132-9
• 发表日期: 2017
• 页码: 71-111
• 关键词: epi-convergent discretizations; residual minimization method; computing equilibria; optimization; PROGRAMS; MARKETS; models

摘要

We propose a two-stage stochastic variational inequality model to deal with random variables in variational inequalities, and formulate this model as a two-stage stochastic programming with recourse by using an expected residual minimization solution procedure. The solvability, differentiability and convexity of the two-stage stochastic programming and the convergence of its sample average approximation are established. Examples of this model are given, including the optimality conditions for stochastic programs, a Walras equilibrium problem and Wardrop flow equilibrium. We also formulate stochastic traffic assignments on arcs flow as a two-stage stochastic variational inequality based on Wardrop flow equilibrium and present numerical results of the Douglas-Rachford splitting method for the corresponding two-stage stochastic programming with recourse.