A theorem of the alternative with an arbitrary number of inequalities and quadratic programming

M. Ruiz Galan

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arXiv · 1610.00888

A theorem of the alternative with an arbitrary number of inequalities and quadratic programming

M. Ruiz Galan

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Abstract

In this paper we are concerned with a Gordan-type theorem involving an arbitrary number of inequality functions. We not only state its validity under a weak convexity assumption on the functions, but also show it is an optimal result. We discuss generalizations of several recent results on nonlinear quadratic optimization, as well as a formula for the Fenchel conjugate of the supremum of a family of functions, in order to illustrate the applicability of that theorem of the alternative.

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M. Ruiz Galan. 2016-10-04. A theorem of the alternative with an arbitrary number of inequalities and quadratic programming. https://arxiv.org/abs/1610.00888

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