Copositivity and constrained fractional quadratic problems

We provide Completely Positive and Copositive Optimization formulations for the Constrained Fractional Quadratic Problem (CFQP) and Standard Fractional Quadratic Problem (StFQP). Based on these formulations, Semidefinite Programming relaxations are derived for finding good lower bounds to these frac...

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Published in	Mathematical programming Vol. 146; no. 1-2; pp. 325 - 350
Main Authors	Amaral, Paula, Bomze, Immanuel M., Júdice, Joaquim
Format	Journal Article
Language	English
Published	Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2014 Springer Nature B.V
Subjects	Algorithms Analysis Calculus of Variations and Optimal Control; Optimization Combinatorics Constraints Eigenvalues Full Length Paper Linear algebra Linear systems Lower bounds Mathematical analysis Mathematical and Computational Physics Mathematical Methods in Physics Mathematical programming Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Optimization Quadratic programming Studies Theoretical 90C30 Nonlinear programming 90C25 Convex programming 90C22 Semidefinite programming 90C26 Nonconvex programming, global optimization 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) 90C32 Fractional programming
Online Access	Get full text
ISSN	0025-5610 1436-4646
DOI	10.1007/s10107-013-0690-8

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Abstract	We provide Completely Positive and Copositive Optimization formulations for the Constrained Fractional Quadratic Problem (CFQP) and Standard Fractional Quadratic Problem (StFQP). Based on these formulations, Semidefinite Programming relaxations are derived for finding good lower bounds to these fractional programs, which can be used in a global optimization branch-and-bound approach. Applications of the CFQP and StFQP, related with the correction of infeasible linear systems and eigenvalue complementarity problems are also discussed.
AbstractList	We provide Completely Positive and Copositive Optimization formulations for the Constrained Fractional Quadratic Problem (CFQP) and Standard Fractional Quadratic Problem (StFQP). Based on these formulations, Semidefinite Programming relaxations are derived for finding good lower bounds to these fractional programs, which can be used in a global optimization branch-and-bound approach. Applications of the CFQP and StFQP, related with the correction of infeasible linear systems and eigenvalue complementarity problems are also discussed. We provide Completely Positive and Copositive Optimization formulations for the Constrained Fractional Quadratic Problem (CFQP) and Standard Fractional Quadratic Problem (StFQP). Based on these formulations, Semidefinite Programming relaxations are derived for finding good lower bounds to these fractional programs, which can be used in a global optimization branch-and-bound approach. Applications of the CFQP and StFQP, related with the correction of infeasible linear systems and eigenvalue complementarity problems are also discussed.[PUBLICATION ABSTRACT]
Author	Bomze, Immanuel M. Júdice, Joaquim Amaral, Paula
Author_xml	– sequence: 1 givenname: Paula surname: Amaral fullname: Amaral, Paula organization: DM, Universidade Nova de Lisboa – sequence: 2 givenname: Immanuel M. surname: Bomze fullname: Bomze, Immanuel M. email: immanuel.bomze@univie.ac.at organization: ISOR, University of Vienna – sequence: 3 givenname: Joaquim surname: Júdice fullname: Júdice, Joaquim organization: DM, Universidade de Coimbra and Instituto de Telecomunicações
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SubjectTerms	Algorithms Analysis Calculus of Variations and Optimal Control; Optimization Combinatorics Constraints Eigenvalues Full Length Paper Linear algebra Linear systems Lower bounds Mathematical analysis Mathematical and Computational Physics Mathematical Methods in Physics Mathematical programming Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Optimization Quadratic programming Studies Theoretical
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Title	Copositivity and constrained fractional quadratic problems
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