Outcome-space branch-and-bound outer approximation algorithm for a class of non-convex quadratic programming problems

The quadratically constrained quadratic programming problem often appears in various fields such as engineering practice, management science and network communication. This paper mainly considers a non-convex quadratic programming problem with convex quadratic constraints. Firstly, the objective fun...

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Vydané v:Journal of global optimization Ročník 86; číslo 1; s. 61 - 92
Hlavní autori: Zhang, Bo, Gao, YueLin, Liu, Xia, Huang, XiaoLi
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.05.2023
Springer
Springer Nature B.V
Predmet:
Algorithms
Approximation
Computer Science
Constraints
Eigenvalues
Equivalence
Feasibility
Global optimization
Investment analysis
Linear functions
Linear programming
Management science
Mathematical optimization
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Optimization algorithms
Quadratic programming
Real Functions
90C20
Branch-and-bound
Global optimization
90C30
Outcome space
Quadratic program
90C26
ISSN:0925-5001, 1573-2916
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Shrnutí:The quadratically constrained quadratic programming problem often appears in various fields such as engineering practice, management science and network communication. This paper mainly considers a non-convex quadratic programming problem with convex quadratic constraints. Firstly, the objective function of the problem is reconstructed into a form composed of only one convex function and several linear functions by using the eigenvalue decomposition technique of matrix. Then the reconstructed problem is converted to the equivalent problem with simple concave quadratic objective function in the outcome space by introducing appropriate auxiliary variables, and its feasible domain is convex. Based on the branch-and-bound framework which can guarantee the global optimality of the solution, a global optimization algorithm for solving the equivalent problem is proposed, which integrates the effective relaxation process and the branching process related to the outer approximation technique. Finally, the effectiveness and feasibility of the algorithm are illustrated by numerical experiments.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-022-01255-8