Metadata only
Date
2023-09-25Type
- Journal Article
Abstract
Adjustable robust minimization problems where the objective or constraints depend in a convex way on the adjustable variables are generally difficult to solve. In this paper, we reformulate the original adjustable robust nonlinear problem with a polyhedral uncertainty set into an equivalent adjustable robust linear problem, for which all existing approaches for adjustable robust linear problems can be used. The reformulation is obtained by first dualizing over the adjustable variables and then over the uncertain parameters. The polyhedral structure of the uncertainty set then appears in the linear constraints of the dualized problem, and the nonlinear functions of the adjustable variables in the original problem appear in the uncertainty set of the dualized problem. We show how to recover linear decision rules to the original primal problem and how to generate bounds on its optimal objective value. Show more
Publication status
publishedExternal links
Journal / series
Operations ResearchVolume
Pages / Article No.
Publisher
INFORMSSubject
Optimization; Adjustable robust optimization; nonlinear inequalities; duality; linear decision rulesMore
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