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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Published inJournal of optimization theory and applications Vol. 170; no. 3; pp. 838 - 852
Main Authors Montiel Lopez, P, Ruiz Galan, M
Format Journal Article
LanguageEnglish
Published New York Springer US 01.09.2016
Springer Nature B.V
Subjects
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
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Summary: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.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-016-0959-1