A Global Optimization Algorithm for Solving Linearly Constrained Quadratic Fractional Problems

This paper first proposes a new and enhanced second order cone programming relaxation using the simultaneous matrix diagonalization technique for the linearly constrained quadratic fractional programming problem. The problem has wide applications in statics, economics and signal processing. Thus, fa...

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Autores principales:	Zhijun Xu, Jing Zhou
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	second order cone programming relaxation copositive relaxation branch-and-bound algorithm global optimization Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/d718036806cc4f86b4005816a5bfb8c2
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id	oai:doaj.org-article:d718036806cc4f86b4005816a5bfb8c2
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spelling	oai:doaj.org-article:d718036806cc4f86b4005816a5bfb8c22021-11-25T18:17:46ZA Global Optimization Algorithm for Solving Linearly Constrained Quadratic Fractional Problems10.3390/math92229812227-7390https://doaj.org/article/d718036806cc4f86b4005816a5bfb8c22021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2981https://doaj.org/toc/2227-7390This paper first proposes a new and enhanced second order cone programming relaxation using the simultaneous matrix diagonalization technique for the linearly constrained quadratic fractional programming problem. The problem has wide applications in statics, economics and signal processing. Thus, fast and effective algorithm is required. The enhanced second order cone programming relaxation improves the relaxation effect and computational efficiency compared to the classical second order cone programming relaxation. Moreover, although the bound quality of the enhanced second order cone programming relaxation is worse than that of the copositive relaxation, the computational efficiency is significantly enhanced. Then we present a global algorithm based on the branch and bound framework. Extensive numerical experiments show that the enhanced second order cone programming relaxation-based branch and bound algorithm globally solves the problem in less computing time than the copositive relaxation approach.Zhijun XuJing ZhouMDPI AGarticlesecond order cone programming relaxationcopositive relaxationbranch-and-bound algorithmglobal optimizationMathematicsQA1-939ENMathematics, Vol 9, Iss 2981, p 2981 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	second order cone programming relaxation copositive relaxation branch-and-bound algorithm global optimization Mathematics QA1-939
spellingShingle	second order cone programming relaxation copositive relaxation branch-and-bound algorithm global optimization Mathematics QA1-939 Zhijun Xu Jing Zhou A Global Optimization Algorithm for Solving Linearly Constrained Quadratic Fractional Problems
description	This paper first proposes a new and enhanced second order cone programming relaxation using the simultaneous matrix diagonalization technique for the linearly constrained quadratic fractional programming problem. The problem has wide applications in statics, economics and signal processing. Thus, fast and effective algorithm is required. The enhanced second order cone programming relaxation improves the relaxation effect and computational efficiency compared to the classical second order cone programming relaxation. Moreover, although the bound quality of the enhanced second order cone programming relaxation is worse than that of the copositive relaxation, the computational efficiency is significantly enhanced. Then we present a global algorithm based on the branch and bound framework. Extensive numerical experiments show that the enhanced second order cone programming relaxation-based branch and bound algorithm globally solves the problem in less computing time than the copositive relaxation approach.
format	article
author	Zhijun Xu Jing Zhou
author_facet	Zhijun Xu Jing Zhou
author_sort	Zhijun Xu
title	A Global Optimization Algorithm for Solving Linearly Constrained Quadratic Fractional Problems
title_short	A Global Optimization Algorithm for Solving Linearly Constrained Quadratic Fractional Problems
title_full	A Global Optimization Algorithm for Solving Linearly Constrained Quadratic Fractional Problems
title_fullStr	A Global Optimization Algorithm for Solving Linearly Constrained Quadratic Fractional Problems
title_full_unstemmed	A Global Optimization Algorithm for Solving Linearly Constrained Quadratic Fractional Problems
title_sort	global optimization algorithm for solving linearly constrained quadratic fractional problems
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/d718036806cc4f86b4005816a5bfb8c2
work_keys_str_mv	AT zhijunxu aglobaloptimizationalgorithmforsolvinglinearlyconstrainedquadraticfractionalproblems AT jingzhou aglobaloptimizationalgorithmforsolvinglinearlyconstrainedquadraticfractionalproblems AT zhijunxu globaloptimizationalgorithmforsolvinglinearlyconstrainedquadraticfractionalproblems AT jingzhou globaloptimizationalgorithmforsolvinglinearlyconstrainedquadraticfractionalproblems
_version_	1718411409037983744

A Global Optimization Algorithm for Solving Linearly Constrained Quadratic Fractional Problems

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