Extending the Scope of Robust Quadratic Optimization

Ahmadreza Marandi (), Aharon Ben-Tal (), Dick den Hertog () and Bertrand Melenberg ()
Additional contact information
Ahmadreza Marandi: Department of Industrial Engineering and Innovation Sciences, Eindhoven University of Technology, Eindhoven 5600 MB, Netherlands
Aharon Ben-Tal: CentER, Tilburg University, Tilburg 5037 AB, Netherlands
Dick den Hertog: Amsterdam Business School, University of Amsterdam, Amsterdam 1012 WX, Netherlands
Bertrand Melenberg: Tilburg School of Economics and Management, Tilburg University, Tilburg 5037 AB, Netherlands

INFORMS Journal on Computing, 2022, vol. 34, issue 1, 211-226

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.

Keywords: robust optimization; quadratic optimization; inner approximation; outer approximation; mean-variance uncertainty (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://dx.doi.org/10.1287/ijoc.2021.1059 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:34:y:2022:i:1:p:211-226

Access Statistics for this article

More articles in INFORMS Journal on Computing from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().