Copositivity and constrained fractional quadratic problems

Paula Amaral; Immanuel Bomze; Joaquim João Júdice

doi:10.1007/s10107-013-0690-8

Copositivity and constrained fractional quadratic problems

Paula Amaral
, Immanuel Bomze (Corresponding author)
, Joaquim João Júdice

Department of Statistics and Operations Research

Publications: Contribution to journal › Article › Peer Reviewed

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
Early online date	23 Jun 2013
DOIs	https://doi.org/10.1007/s10107-013-0690-8
Publication status	Published - Aug 2014

Austrian Fields of Science 2012

101015 Operations research

Keywords

ISOR
90C30 Nonlinear programming
90C25 Convex programming
Mathematics Subject Classification (2010): 90C22 Semidefinite programming
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions)
90C32 Fractional programming
90C26 Nonconvex programming, global optimization

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10.1007/s10107-013-0690-8

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title = "Copositivity and constrained fractional quadratic problems",

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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author = "Paula Amaral and Immanuel Bomze and J{\'u}dice, \{Joaquim Jo{\~a}o\}",

year = "2014",

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doi = "10.1007/s10107-013-0690-8",

language = "English",

volume = "146",

pages = "325--350",

journal = "Mathematical Programming",

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TY - JOUR

T1 - Copositivity and constrained fractional quadratic problems

AU - Amaral, Paula

AU - Bomze, Immanuel

AU - Júdice, Joaquim João

PY - 2014/8

Y1 - 2014/8

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 - ISOR

KW - 90C30 Nonlinear programming

KW - 90C25 Convex programming

KW - Mathematics Subject Classification (2010): 90C22 Semidefinite programming

KW - 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions)

KW - 90C32 Fractional programming

KW - 90C26 Nonconvex programming, global optimization

UR - https://www.scopus.com/pages/publications/84905572321

U2 - 10.1007/s10107-013-0690-8

DO - 10.1007/s10107-013-0690-8

M3 - Article

SN - 0025-5610

VL - 146

SP - 325

EP - 350

JO - Mathematical Programming

JF - Mathematical Programming

IS - 1-2

ER -

Copositivity and constrained fractional quadratic problems

Abstract

Austrian Fields of Science 2012

Keywords

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