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Technical Note—Dual Approach for Two-Stage Robust Nonlinear Optimization

Author

Listed:
  • Frans J. C. T. de Ruiter

    (Operations Research and Logistics Group, Wageningen University and Research, 6706 KN Wageningen, Netherlands)

  • Jianzhe Zhen

    (Risk Analytics and Optimization Chair, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland; Automatic Control Laboratory, Eidgenössische Technische Hochschule Zürich, 8092 Zürich, Switzerland)

  • Dick den Hertog

    (Amsterdam Business School, University of Amsterdam, 1001 NL Amsterdam, Netherlands)

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.

Suggested Citation

  • Frans J. C. T. de Ruiter & Jianzhe Zhen & Dick den Hertog, 2023. "Technical Note—Dual Approach for Two-Stage Robust Nonlinear Optimization," Operations Research, INFORMS, vol. 71(5), pages 1794-1799, September.
    • Handle: RePEc:inm:oropre:v:71:y:2023:i:5:p:1794-1799
    DOI: 10.1287/opre.2022.2289
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