Nonlinear Programming via König’s Maximum Theorem

Starting from one extension of the Hahn–Banach theorem, the Mazur–Orlicz theorem, and a not very restrictive concept of convexity, that arises naturally in minimax theory, infsup-convexity, we derive an equivalent version of that fundamental result for finite dimensional spaces, which is a sharp gen...

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Podrobná bibliografie
Vydáno v:	Journal of optimization theory and applications Ročník 170; číslo 3; s. 838 - 852
Hlavní autoři:	Montiel Lopez, P, Ruiz Galan, M
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.09.2016 Springer Nature B.V
Témata:	Applications of Mathematics Banach spaces Calculus of Variations and Optimal Control; Optimization Engineering Equivalence Inequalities Inequality Lagrange multiplier Lagrange multipliers Mathematical analysis Mathematics Mathematics and Statistics Minimax technique Nonlinear programming Operations Research/Decision Theory Optimization Studies Theorems Theory of Computation Vector space 90C30 Fritz John theorem 90C46 Lagrange multipliers Karush/Kuhn–Tucker theorem 46A22 Nonlinear programming 26B25 Separation theorem Infsup-convexity Hahn–Banach theorem
ISSN:	0022-3239, 1573-2878
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Popis
Shrnutí:	Starting from one extension of the Hahn–Banach theorem, the Mazur–Orlicz theorem, and a not very restrictive concept of convexity, that arises naturally in minimax theory, infsup-convexity, we derive an equivalent version of that fundamental result for finite dimensional spaces, which is a sharp generalization of König’s Maximum theorem. It implies several optimal statements of the Lagrange multipliers, Karush/Kuhn–Tucker, and Fritz John type for nonlinear programs with an objective function subject to both equality and inequality constraints.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23
ISSN:	0022-3239 1573-2878
DOI:	10.1007/s10957-016-0959-1