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

Cheng Lu, Zhibin Deng (), Jing Zhou and Xiaoling Guo
Additional contact information
Cheng Lu: North China Electric Power University
Zhibin Deng: Chinese Academy of Sciences
Jing Zhou: Zhejiang University of Technology
Xiaoling Guo: China University of Mining and Technology

Journal of Global Optimization, 2019, vol. 73, issue 2, No 6, 388 pages

Abstract: 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.

Keywords: Quadratically constrained quadratic programming; Semidefinite relaxation; Branch-and-bound algorithm; Global optimization (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10898-018-0726-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jglopt:v:73:y:2019:i:2:d:10.1007_s10898-018-0726-y

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-018-0726-y

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

More articles in Journal of Global Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().