Séminaire Mathématique de Béjaia
Volume 16, Numéro 1, Pages 87-87
2018-12-31

Nonconvex Quadratic Minimization With One Negative Eigenvalue



Authors : Andjouh Amar . Bibi Mohand Ouamer .

Abstract

This project provides a new support method of global optimization to solve the quadratic minimization problem with one negative eigenvalue, subject to box constraints. We investigate the support of the objective function and exploit properties of the indefinite associated matrix for finding global optimality criterion (necessary and sufficient conditions). Furthermore, using these conditions and computational techniques, we apply the support method that can effectively solve a quadratic minimization problem with an indefinite associated matrix, having one negative eigenvalue. Particularly, we study the case where the associated matrix is positive subdefinite, and we use the suggested support algorithm in order to find the optimal solution. We present numerical applications to solve some box-constrained nonconvex problems with one negative eigenvalue.

Keywords

Quadratic Minimization with One Negative Eigenvalue; Global Optimality Criterion; Merely Positive SubDefinite matrix (MPSubD).

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