Titel
Interplay of non-convex quadratically constrained problems with adjustable robust optimization
Autor*in
Abstract
In this paper we explore convex reformulation strategies for non-convex quadratically constrained optimization problems (QCQPs). First we investigate such reformulations using Pataki’s rank theorem iteratively. We show that the result can be used in conjunction with conic optimization duality in order to obtain a geometric condition for the S-procedure to be exact. Based upon known results on the S-procedure, this approach allows for some insight into the geometry of the joint numerical range of the quadratic forms. Then we investigate a reformulation strategy introduced in recent literature for bilinear optimization problems which is based on adjustable robust optimization theory. We show that, via a similar strategy, one can leverage exact reformulation results of QCQPs in order to derive lower bounds for more complicated quadratic optimization problems. Finally, we investigate the use of reformulation strategies in order to derive characterizations of set-copositive matrix cones. Empirical evidence based upon first numerical experiments shows encouraging results.
Stichwort
Robust optimizationQuadratic optimizationConic optimizationS-LemmaCopositivity
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
phaidra.univie.ac.at/o:1218534
Erschienen in
Titel
Mathematical Methods of Operations Research
Band
93
ISSN
1432-2994
Erscheinungsdatum
2020
Seitenanfang
115
Seitenende
151
Publication
Springer Science and Business Media LLC
Fördergeber
Austrian Science Fund (FWF) — W 1260-N35
Erscheinungsdatum
2020
Zugänglichkeit
Rechte
Rechteangabe
© The Author(s) 2020
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