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Extending the Scope of Robust Quadratic Optimization.
- Source :
-
INFORMS Journal on Computing . Winter2022, Vol. 34 Issue 1, p211-226. 16p. - Publication Year :
- 2022
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ROBUST optimization
*COVARIANCE matrices
Subjects
Details
- Language :
- English
- ISSN :
- 10919856
- Volume :
- 34
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- INFORMS Journal on Computing
- Publication Type :
- Academic Journal
- Accession number :
- 155827906
- Full Text :
- https://doi.org/10.1287/ijoc.2021.1059