Quadratic convex reformulation for nonconvex binary quadratically constrained quadratic programming via surrogate constraint

We investigate in this paper nonconvex binary quadratically constrained quadratic programming (QCQP) which arises in various real-life fields. We propose a novel approach of getting quadratic convex reformulation (QCR) for this class of optimization problem. Our approach employs quadratic surrogate...

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Vydáno v:Journal of global optimization Ročník 70; číslo 4; s. 719 - 735
Hlavní autoři: Zheng, Xiaojin, Pan, Yutong, Cui, Xueting
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.04.2018
Springer
Springer Nature B.V
Témata:
Computer Science
Constraints
Mathematics
Mathematics and Statistics
Nonlinear programming
Operations Research/Decision Theory
Optimization
Quadratic programming
Real Functions
Semidefinite programming
Binary QCQP
Semidefinite programming
Global optimization
Quadratic convex reformulation
ISSN:0925-5001, 1573-2916
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Shrnutí:We investigate in this paper nonconvex binary quadratically constrained quadratic programming (QCQP) which arises in various real-life fields. We propose a novel approach of getting quadratic convex reformulation (QCR) for this class of optimization problem. Our approach employs quadratic surrogate functions and convexifies all the quadratic inequality constraints to construct QCR. The price of this approach is the introduction of an extra quadratic inequality. The “best” QCR among the proposed family, in terms that the bound of the corresponding continuous relaxation is best, can be found via solving a semidefinite programming problem. Furthermore, we prove that the bound obtained by continuous relaxation of our best QCR is as tight as Lagrangian bound of binary QCQP. Computational experiment is also conducted to illustrate the solution efficiency improvement of our best QCR when applied in off-the-shell software.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-017-0591-0