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

M. Ruiz Galán ()
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M. Ruiz Galán: University of Granada

Journal of Global Optimization, 2017, vol. 69, issue 2, No 6, 427-442

Abstract: 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.

Keywords: Theorems of the alternative; Quadratic programming; Separation theorem; Infsup-convexity; 90C46; 90C20; 46A22; 26B25 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10898-017-0525-x

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