Mathematical properties of optimization problems defined by positively homgeneous functions

Authors:
J. B. Lasserre;J. B. Hiriart-Urruty
Affiliations:
Directeur de Recherche, LAAS-CNRS, Toulouse, France;Professeur, Département de Mathématiques, Université Paul Sabatier, Toulouse, France
Venue:
Journal of Optimization Theory and Applications
Year:
2002

Citing 6
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Abstract

We consider the nonlinear programming problem (P) → {minf(x)|gi(x) ≤ bi, i=1,...,m}, with f positively p-homogeneous and gi positively q-homogeneous functions. We show that (P) admits a simple min-max formulation (D) with the inner max-problem being a trivial linear program with a single constraint. This provides a new formulation of the linear programming problem and the linear-quadratic one as well. In particular, under some conditions, a global (nonconvex) optimization problem with quadratic data is shown to be equivalent to a convex minimization problem.