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Robust optimization for models with uncertain SOC and SDP constraints

Jianzhe Zhen (jianzhe.zhen***at***epfl.ch)
Frans J.C.T. de Ruiter (fjctderuiter***at***gmail.com)
Dick den Hertog (d.denHertog***at***uvt.nl)

Abstract: In this paper we consider uncertain second-order cone (SOC) and semidefinite programming (SDP) constraints with polyhedral uncertainty. We propose to reformulate an uncertain SOC or SDP constraint as a set of adjustable robust linear optimization constraints with an ellipsoidal or semidefinite representable uncertainty set, respectively. The resulting adjustable problem can then (approximately) be solved by using adjustable robust linear optimization techniques. For example, we show that if linear decision rules are used, then the final robust counterpart consists of SOC or SDP constraints, respectively, which have the same computational complexity as the nominal version with the original constraints. We also propose an efficient method to obtain good lower bounds, and extend our approach to other classes of robust optimization problems. Finally, we apply our approach to a robust regression problem and a robust sensor network problem. We use linear decision rules to solve the resulting adjustable robust linear optimization problems and the solutions found are optimal or near optimal.

Keywords: Robust optimization, second-order cone, semidefinite programming, adjustable robust optimization, linear decision rules.

Category 1: Robust Optimization


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Entry Submitted: 12/11/2017
Entry Accepted: 12/11/2017
Entry Last Modified: 03/07/2018

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