Discrete approximation of two-stage stochastic and distributionally robust linear complementarity problems

• 成果类型: Article
• 署名作者: Chen, Xiaojun; Sun, Hailin; Xu, Huifu
• 署名单位: Hong Kong Polytechnic University; Nanjing University of Science & Technology; University of Southampton
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-018-1266-4
• 发表日期: 2019
• 页码: 255-289
• 关键词: variational-inequalities; CONVERGENCE; PROGRAMS; bounds

摘要

In this paper, we propose a discretization scheme for the two-stage stochastic linear complementarity problem (LCP) where the underlying random data are continuously distributed. Under some moderate conditions, we derive qualitative and quantitative convergence for the solutions obtained from solving the discretized two-stage stochastic LCP (SLCP). We explain how the discretized two-stage SLCP may be solved by the well-known progressive hedging method (PHM). Moreover, we extend the discussion by considering a two-stage distributionally robust LCP (DRLCP) with moment constraints and proposing a discretization scheme for the DRLCP. As an application, we show how the SLCP and DRLCP models can be used to study equilibrium arising from two-stage duopoly game where each player plans to set up its optimal capacity at present with anticipated competition for production in future.