Copositivity and constrained fractional quadratic problems

Paula Amaral; Immanuel M. Bomze; Joaquim Judice

doi:10.1007/s10107-013-0690-8

Copositivity and constrained fractional quadratic problems

Paula Amaral, Immanuel M. Bomze, Joaquim Judice

DM - Departamento de Matemática

Research output: Contribution to journal › Article

16 Citations (Scopus)

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.

Original language	English
Pages (from-to)	325-350
Number of pages	26
Journal	Mathematical Programming
Volume	146
Issue number	1-2
DOIs	https://doi.org/10.1007/s10107-013-0690-8
Publication status	Published - Aug 2014

Keywords

TOTAL LEAST-SQUARES
EIGENVALUE COMPLEMENTARITY-PROBLEM
OPTIMIZATION PROBLEMS
GLOBAL OPTIMIZATION
SEMIDEFINITE
ALGORITHM
PROGRAMS
MOMENTS
SYSTEM
NUMBER

Cite this

Amaral, P., Bomze, I. M., & Judice, J. (2014). Copositivity and constrained fractional quadratic problems. Mathematical Programming, 146(1-2), 325-350. https://doi.org/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.",

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AU - Amaral, Paula

AU - Bomze, Immanuel M.

AU - Judice, Joaquim

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N2 - 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.

AB - 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.

KW - TOTAL LEAST-SQUARES

KW - EIGENVALUE COMPLEMENTARITY-PROBLEM

KW - OPTIMIZATION PROBLEMS

KW - GLOBAL OPTIMIZATION

KW - SEMIDEFINITE

KW - ALGORITHM

KW - PROGRAMS

KW - MOMENTS

KW - SYSTEM

KW - NUMBER

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DO - 10.1007/s10107-013-0690-8

M3 - Article

VL - 146

SP - 325

EP - 350

JO - Mathematical Programming

JF - Mathematical Programming

SN - 0025-5610

IS - 1-2

ER -

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