Revisiting the Hahn–Banach theorem and nonlinear infinite programming

The aim of this paper is to state a sharp version of the König supremum theorem, an equivalent reformulation of the Hahn–Banach theorem. We apply it to derive statements of the Lagrange multipliers, Karush–Kuhn–Tucker and Fritz John types, for nonlinear infinite programs. We also show that a weak co...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 455; no. 2; pp. 1037 - 1050
Main Authors Montiel López, P., Ruiz Galán, M.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.11.2017
Subjects
Fritz John theorem
Hahn–Banach theorem
Infsup-convexity
Karush–Kuhn–Tucker theorem
Lagrange multipliers
Nonlinear programming
Karush–Kuhn–Tucker theorem
Nonlinear programming
Fritz John theorem
Infsup-convexity
Lagrange multipliers
Hahn–Banach theorem
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ISSN0022-247X
1096-0813
DOI10.1016/j.jmaa.2017.06.007

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Summary:The aim of this paper is to state a sharp version of the König supremum theorem, an equivalent reformulation of the Hahn–Banach theorem. We apply it to derive statements of the Lagrange multipliers, Karush–Kuhn–Tucker and Fritz John types, for nonlinear infinite programs. We also show that a weak concept of convexity coming from minimax theory, infsup-convexity, is the adequate one for this kind of results.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2017.06.007