Improved Decision Rule Approximations for Multistage Robust Optimization via Copositive Programming

• 成果类型: Article
• 署名作者: Xu, Guanglin; Hanasusanto, Grani A.
• 署名单位: University of North Carolina; University of North Carolina Charlotte; University of Minnesota System; University of Minnesota Twin Cities; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2018.0505
• 发表日期: 2025
• 关键词: PORTFOLIO OPTIMIZATION; linear-programs; affine policies; semidefinite; uncertainty; DESIGN; binary

摘要

We study decision rule approximations for generic multistage robust linear optimization problems. We examine linear decision rules for the case when the objective coefficients, the recourse matrices, and the right-hand sides are uncertain, and we explore quadratic decision rules for the case when only the right-hand sides are uncertain. The resulting optimization problems are NP hard but amenable to copositive programming reformulations that give rise to tight, tractable semidefinite programming solution approaches. We further enhance these approximations through new piecewise decision rule schemes. Finally, we prove that our proposed approximations are tighter than the state-of-the-art schemes and demonstrate their superiority through numerical experiments.