Conic optimization: a survey with special focus on copositive optimization and binary quadratic problems

  • A conic optimization problem is a problem involving a constraint that the optimization variable be in some closed convex cone. Prominent examples are linear programs (LP), second order cone programs (SOCP), semidefinite problems (SDP), and copositive problems. We survey recent progress made in this area. In particular, we highlight the connections between nonconvex quadratic problems, binary quadratic problems, and copositive optimization. We review how tight bounds can be obtained by relaxing the copositivity constraint to semidefiniteness, and we discuss the effect that different modelling techniques have on the quality of the bounds. We also provide some new techniques for lifting linear constraints and show how these can be used for stable set and coloring relaxations.

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Metadaten
Author:Mirjam DürGND, Franz Rendl
URN:urn:nbn:de:bvb:384-opus4-1226398
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/122639
ISSN:2192-4406OPAC
Parent Title (English):EURO Journal on Computational Optimization
Publisher:Elsevier BV
Place of publication:Amsterdam
Type:Article
Language:English
Year of first Publication:2021
Publishing Institution:Universität Augsburg
Release Date:2025/06/06
Volume:9
First Page:100021
DOI:https://doi.org/10.1016/j.ejco.2021.100021
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Diskrete Mathematik, Optimierung und Operations Research
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):CC-BY 4.0: Creative Commons: Namensnennung (mit Print on Demand)

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