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2889. Solution of Fractional Quadratic Programs on the Simplex
Invited abstract in session WD-43: Recent advances on Variational Inequalities and Equilibrium Problems III , stream Variational Inequalities and Equilibrium Problems: From Theoretical Advances to Real World Applications.
Wednesday, 14:30-16:00Room: 99 (building: 306)
Authors (first author is the speaker)
| 1. | Valentina Sessa
|
| Centre for Applied Mathematics, Mines Paris - PSL |
Abstract
We deal with the Standard Fractional Quadratic Quadratic Programming Problem (StFQQP), consisting of the minimization of the ratio of two quadratic functions over the standard simplex. We assume the denominator is strictly convex with a symmetric positive definitive (SPD) matrix, so the objective function is well-defined on the feasible set.
Without loss of generality, we also assume the numerator is strictly convex with an SPD matrix.
Contrary to the case where the numerator is a linear function, a stationary point (SP) of StFQQP is not necessarily a global minimum because the objective function is not quasi-convex.
We introduce a new sequential algorithm for the StFQQP, exploiting a reformulation as a mathematical program with complementarity constraints derived from the KKT conditions of the StFQQP, which are in the form of the so-called symmetric Eigenvalue Complementarity Problem (EiCP). Solving an EiCP is then equivalent to computing an SP to the StFQQP.
Preliminary computational experiments with various test problems suggest that the sequential algorithm is a promising technique for solving the StFQQP.
Keywords
- Algorithms
- Continuous Optimization
Status: accepted
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