Robust Solutions to a System of Stochastic Vertical Linear Complementarity Problems

• 成果类型: Article; Early Access
• 署名作者: Zha, Xiao; Allen-Zhao, Zhihua; Chen, Xiaojun
• 署名单位: Hong Kong Polytechnic University; Xidian University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.2024.0856
• 发表日期: 2025-12-17
• 关键词: stochastic linear complementarity problem; discrete smoothing approximation; exact penalization; convergence analysis; PORTFOLIO SELECTION; mathematical programs; equilibrium constraints; optimization; nonsmooth; CONVERGENCE; algorithm; Penalty

摘要

We propose a stochastic minimization model to find a robust solution of a system of stochastic vertical linear complementarity problems. This model aims to minimize a risk function under stochastic vertical linear complementarity constraints. We reformulate the model with a finite support set as a linearly constrained piecewise smooth minimization problem by a penalty method. We prove the existence of exact penalty parameters regarding global and local minimizers. We define a smoothing function of the piecewise smooth objective function and show that the smoothing function satisfies the Kurdyka-& Lstrok;ojasiewicz (KL) property. Moreover, we propose a smoothing block coordinate descent algorithm and prove that the sequence generated by the algorithm globally converges to an epsilon-Clarke stationary point of the penalty problem by the KL property for any epsilon > 0. Finally, we apply our model and algorithm to portfolio selection problems with real data. Numerical results demonstrate the robustness of our model.