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Approximation of hard uncertain convex inequalities

Ernst Roos (e.j.roos***at***tilburguniversity.edu)
Dick den Hertog (d.denhertog***at***tilburguniversity.edu)
Aharon Ben-Tal (abental***at***technion.ac.il)
Frans de Ruiter (fjctderuiter***at***gmail.com)
Jianzhe Zhen (trevorzhen***at***gmail.com)

Abstract: Robust Optimization is a widespread approach to treat uncertainty in optimization problems. Finding a computationally tractable formulation of the robust counterpart of an uncertain optimization problem is a key step in applying this approach. Although techniques for finding a robust counterpart are available for many types of constraints, no general techniques exist for problems requiring maximizing functions that are convex in the uncertain parameters. Such constraints are, however, quite common. In this paper, we treat these hard problems and provide a systematic way to construct a safe approximation to their robust counterpart given a polyhedral uncertainty set. We use convex analysis as well as adjustable robust optimization techniques to obtain these approximations. We demonstrate the quality of the approximations by performing numerical experiments.

Keywords: Robust optimization, adjustable robust optimization, linear decision rules, nonlinear inequalities

Category 1: Robust Optimization


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Entry Submitted: 06/27/2018
Entry Accepted: 06/27/2018
Entry Last Modified: 02/27/2019

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