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Journal of Convex Analysis 25 (2018), No. 2, [final page numbers not yet available]
Copyright Heldermann Verlag 2018

Minimization of Quadratic Functions on Convex Sets without Asymptotes

Juan-Enrique Martinez-Legaz
Dep. d'Economia i d'Història Econòmica, Universitat Autónoma de Barcelona, 08193 Bellaterra, Spain

Dominikus Noll
Institut de Mathématiques, Université de Toulouse, 118 route de Narbonne, 31062 Toulouse, France

Wilfredo Sosa
Programa de Pôs-Graduação em Economia, Universidade Católica de Brasilia, Brazil

The classical Frank and Wolfe theorem states that a quadratic function which is bounded below on a convex polyhedron P attains its infimum on P. We investigate whether more general classes of convex sets F can be identified which have this Frank-and-Wolfe property. We show that the intrinsic characterizations of Frank-and-Wolfe sets hinge on asymptotic properties of these sets.

Keywords: Quadratic optimization problem, asymptotes, conic asymptotes, Motzkin decomposition, Frank and Wolfe theorem, complementarity problem.

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