Dual Approach for Two-Stage Robust Nonlinear Optimization
成果类型：
Article
署名作者：
de Ruiter, Frans J. C. T.; Zhen, Jianzhe; den Hertog, Dick
署名单位：
Wageningen University & Research; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Amsterdam
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.2022.2289
发表日期：
2023
页码：
1794-1799
关键词：
摘要：
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.
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