Improved Decision Rule Approximations for Multi-Stage Robust Optimization via Copositive Programming

2018/08/19 by Guanglin Xu, Grani A. Hanasusanto, Xu, Guanglin +1 · 1 citation
Business, Management and Accounting · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Mathematical Programming #Supply Chain and Inventory Management

paper · pdf · doi:10.48550/arxiv.1808.06231

openalex publication_date 2018/08/19 · openalex created_date 2023/09/22 · openalex updated_date 2026/07/28

Abstract

We study decision rule approximations for generic multi-stage robust linear optimization problems. We consider linear decision rules for the case when the objective coefficients, the recourse matrices, and the right-hand sides are uncertain, and consider 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 conservative approximations. 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.

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