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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Veröffentlicht in:	Journal of global optimization Jg. 73; H. 2; S. 371 - 388
Hauptverfasser:	Lu, Cheng, Deng, Zhibin, Zhou, Jing, Guo, Xiaoling
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Springer US 15.02.2019 Springer Springer Nature B.V
Schlagworte:	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
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Abstract	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.
AbstractList	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.
Audience	Academic
Author	Deng, Zhibin Guo, Xiaoling Lu, Cheng Zhou, Jing
Author_xml	– sequence: 1 givenname: Cheng surname: Lu fullname: Lu, Cheng organization: School of Economics and Management, North China Electric Power University – sequence: 2 givenname: Zhibin orcidid: 0000-0003-0563-5841 surname: Deng fullname: Deng, Zhibin email: zhibindeng@ucas.ac.cn organization: School of Economics and Management, University of Chinese Academy of Sciences, Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences – sequence: 3 givenname: Jing surname: Zhou fullname: Zhou, Jing organization: Department of Applied Mathematics, College of Science, Zhejiang University of Technology – sequence: 4 givenname: Xiaoling surname: Guo fullname: Guo, Xiaoling organization: Departmemt of Mathematics, China University of Mining and Technology
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CitedBy_id	crossref_primary_10_1016_j_ejco_2022_100040 crossref_primary_10_3390_math10020270 crossref_primary_10_1108_IJQRM_09_2020_0315 crossref_primary_10_1155_2020_5717301 crossref_primary_10_1007_s40305_020_00309_6 crossref_primary_10_1007_s10898_022_01218_z
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Snippet	In this paper, we design an eigenvalue decomposition based branch-and-bound algorithm for finding global solutions of quadratically constrained quadratic...
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SubjectTerms	Algorithms Computer Science Decomposition Eigenvalues Eigenvectors Mathematics Mathematics and Statistics Mechanical properties Operations Research/Decision Theory Optimization Quadratic programming Real Functions
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Title	A sensitive-eigenvector based global algorithm for quadratically constrained quadratic programming
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