Improved Decision Rule Approximations for Multistage Robust Optimization via Copositive Programming

Guanglin Xu () and Grani A. Hanasusanto ()
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Guanglin Xu: Department of Systems Engineering and Engineering Management, University of North Carolina at Charlotte, Charlotte, North Carolina 28270; and Institute for Mathematics and Its Applications, University of Minnesota, Minneapolis, Minnesota 55455
Grani A. Hanasusanto: Department of Industrial and Enterprise Systems Engineering, University of Illinois Urbana–Champaign, Urbana, Illinois 61801

Operations Research, 2025, vol. 73, issue 2, 842-861

Abstract: 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.

Keywords: Optimization; multistage robust optimization; decision rules; piecewise decision rules; conservative approximations; copositive programming; semidefinite programming (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:73:y:2025:i:2:p:842-861

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