Penalized semidefinite programming for quadratically-constrained quadratic optimization

In this paper, we give a new penalized semidefinite programming approach for non-convex quadratically-constrained quadratic programs (QCQPs). We incorporate penalty terms into the objective of convex relaxations in order to retrieve feasible and near-optimal solutions for non-convex QCQPs. We introd...

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Veröffentlicht in:Journal of global optimization Jg. 78; H. 3; S. 423 - 451
Hauptverfasser: Madani, Ramtin, Kheirandishfard, Mohsen, Lavaei, Javad, Atamtürk, Alper
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.11.2020
Springer
Springer Nature B.V
Schlagworte:
Computer Science
Constraints
Feasibility
Iterative methods
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Quadratic programming
Real Functions
Semidefinite programming
System identification
Semidefinite programming
Non-convex optimization
65K05
90C22
90-08
Convex relaxation
90C26
Non-linear programming
ISSN:0925-5001, 1573-2916
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Zusammenfassung:In this paper, we give a new penalized semidefinite programming approach for non-convex quadratically-constrained quadratic programs (QCQPs). We incorporate penalty terms into the objective of convex relaxations in order to retrieve feasible and near-optimal solutions for non-convex QCQPs. We introduce a generalized linear independence constraint qualification (GLICQ) criterion and prove that any GLICQ regular point that is sufficiently close to the feasible set can be used to construct an appropriate penalty term and recover a feasible solution. Inspired by these results, we develop a heuristic sequential procedure that preserves feasibility and aims to improve the objective value at each iteration. Numerical experiments on large-scale system identification problems as well as benchmark instances from the library of quadratic programming demonstrate the ability of the proposed penalized semidefinite programs in finding near-optimal solutions for non-convex QCQP.
Bibliographie:ObjectType-Article-1
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-020-00918-8