A sensitive-eigenvector based global algorithm for quadratically constrained quadratic programming

In this paper, we design an eigenvalue decomposition based branch-and-bound algorithm for finding global solutions of quadratically constrained quadratic programming (QCQP) problems. The hardness of nonconvex QCQP problems roots in the nonconvex components of quadratic terms, which are represented b...

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Bibliographic Details
Published in:Journal of global optimization Vol. 73; no. 2; pp. 371 - 388
Main Authors: Lu, Cheng, Deng, Zhibin, Zhou, Jing, Guo, Xiaoling
Format: Journal Article
Language:English
Published: New York Springer US 15.02.2019
Springer
Springer Nature B.V
Subjects:
Algorithms
Computer Science
Decomposition
Eigenvalues
Eigenvectors
Mathematics
Mathematics and Statistics
Mechanical properties
Operations Research/Decision Theory
Optimization
Quadratic programming
Real Functions
Global optimization
Semidefinite relaxation
Quadratically constrained quadratic programming
Branch-and-bound algorithm
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:In this paper, we design an eigenvalue decomposition based branch-and-bound algorithm for finding global solutions of quadratically constrained quadratic programming (QCQP) problems. The hardness of nonconvex QCQP problems roots in the nonconvex components of quadratic terms, which are represented by the negative eigenvalues and the corresponding eigenvectors in the eigenvalue decomposition. For certain types of QCQP problems, only very few eigenvectors, defined as sensitive-eigenvectors, determine the relaxation gaps. We propose a semidefinite relaxation based branch-and-bound algorithm to solve QCQP. The proposed algorithm, which branches on the directions of the sensitive-eigenvectors, is very efficient for solving certain types of QCQP problems.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-018-0726-y