Extending the scope of robust quadratic optimization
Marandi,A. Ben-Tal,A. den Hertog,Dick Melenberg,Bertrand
Marandi,A.
Ben-Tal,A.
den Hertog,Dick
Melenberg,Bertrand
Abstract
We derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We do this for a broad range of uncertainty sets. Our results provide extensions to known results from the literature. We also consider hard quadratic constraints: those that are convex in uncertain matrix-valued parameters. For the robust counterpart of such constraints, we derive inner and outer tractable approximations. As an application, we show how to construct a natural uncertainty set based on a statistical confidence set around a sample mean vector and covariance matrix and use this to provide a tractable reformulation of the robust counterpart of an uncertain portfolio optimization problem. We also apply the results of this paper to norm approximation problems. Summary of Contribution: This paper develops new theoretical results and algorithms that extend the scope of a robust quadratic optimization problem. More specifically, we derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We also consider hard quadratic constraints: those that are convex in uncertain matrix-valued parameters. For the robust counterpart of such constraints, we derive inner and outer tractable approximations.
Description
Date
2022-01
Journal Title
Journal ISSN
Volume Title
Publisher
Research Projects
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Journal Issue
Keywords
robust optimization, quadratic optimization, inner approximation, outer approximation, mean-variance uncertainty
Citation
Marandi, A, Ben-Tal, A, den Hertog, D & Melenberg, B 2022, 'Extending the scope of robust quadratic optimization', INFORMS Journal on Computing, vol. 34, no. 1, pp. 211-226. https://doi.org/10.1287/ijoc.2021.1059