Copositivity and constrained fractional quadratic problems

• 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
• DOI: 10.1007/s10107-013-0690-8

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.