Robust Quadratic Programming with Mixed-Integer Uncertainty

Can Gokalp (cangokalputexas.edu)
Areesh Mittal (areeshmittalutexas.edu)
Grani A. Hanasusanto (grani.hanasusantoutexas.edu)

Abstract: We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are amenable to exact copositive programming reformulations of polynomial size. These convex optimization problems are NP-hard but admit a conservative semidefinite programming (SDP) approximation that can be solved efficiently. We prove that the popular approximate S-lemma method---which is valid only in the case of continuous uncertainty---is weaker than our approximation. We also show that all results can be extended to the two-stage robust quadratic optimization setting if the problem has complete recourse. We assess the effectiveness of our proposed SDP reformulations and demonstrate their superiority over the state-of-the-art solution schemes on instances of least squares, project management, and multi-item newsvendor problems.

Keywords: robust optimization, quadratic programming, copositive programming, semidefinite programming

Category 1: Robust Optimization

Category 2: Nonlinear Optimization (Quadratic Programming )

Category 3: Linear, Cone and Semidefinite Programming

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Entry Submitted: 06/06/2017
Entry Accepted: 06/06/2017
Entry Last Modified: 05/18/2018

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