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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Bibliographic Details
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
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary: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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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-013-0690-8