A Smooth C-Function-Based ERM Method for Stochastic Symmetric Cone Linear Complementarity Problems

• 成果类型: Article; Early Access
• 署名作者: Tang, Jingyong; Sun, Guo; Zhou, Jinchuan; Zhang, Hongchao
• 署名单位: Xinyang Normal University; Qufu Normal University; Shandong University of Technology; Louisiana State University System; Louisiana State University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.2025.0951
• 发表日期: 2026-05-18
• 关键词: stochastic linear complementarity problems (S-LCP); symmetric cone; complementarity function; ERM formulation; Monte Carlo approximation; RESIDUAL MINIMIZATION FORMULATION; Newton method; algorithm

摘要

This paper considers the stochastic symmetric cone linear complementarity problem (S-SCLCP), which includes the stochastic linear complementarity problem and the stochastic second-order cone linear complementarity problem as special cases. We propose a new expected residual minimization (ERM) formulation for S-SCLCP and apply the Monte Carlo technique to generate the corresponding approximation problem. Different from existing ERM formulations for stochastic complementarity problems, the proposed ERM formulation is based on a smooth C-function and a variant merit function. Relying on the Euclidean Jordan algebra associated with symmetric cones, we address several important issues, including coerciveness, existence of solutions, global convergence, and exponential convergence rate. Furthermore, we present some numerical examples and the practical applications of ERM schemes in solving an uncertain Nash-Cournot game and a stochastic optimal power flow problem in the radial network, demonstrating the effectiveness of this method.