Abstract
This article deals with systems of infinitely many inequalities involving functions that are positively homogeneous over a nonempty convex cone of the Euclidean space. Generalized convex conjugation theory is applied to derive a Farkas-type and a Gale-type theorem for this kind of systems. These results are particularized for linear and min-type inequality systems.
Acknowledgments
The research of the first author has been partially supported by the Spanish Ministry of Science and Technology, project BFM2002-04114-C02, and by the sabbatical program of Alicante University. The work of the second author has been supported by the Spanish Ministry of Science and Technology, project BEC2002-00642, and by the Departament d'Universitats, Recerca i Societat de la Informació, Direcció General de Recerca de la Generalitat de Catalunya, project 2001SGR-00162. He also thanks the support of the Barcelona Economics Program of CREA.
Notes
Dedicated to V.F. Demyanov on the occasion of his 65th birthday.
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