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

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...

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Bibliographic Details
Published inJournal of global optimization Vol. 69; no. 2; pp. 427 - 442
Main Author Ruiz Galán, M.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.10.2017
Springer
Springer Nature B.V
Subjects
Computer Science
Convexity
Inequalities
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Quadratic programming
Real Functions
Theorems
90C20
90C46
46A22
Theorems of the alternative
26B25
Quadratic programming
Separation theorem
Infsup-convexity
Online AccessGet full text
ISSN0925-5001
1573-2916
DOI10.1007/s10898-017-0525-x

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Summary: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.
Bibliography:ObjectType-Article-1
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-017-0525-x