Nonlinear Programming via König’s Maximum Theorem

P. Montiel López () and M. Ruiz Galán ()
Additional contact information
P. Montiel López: University of Granada
M. Ruiz Galán: University of Granada

Journal of Optimization Theory and Applications, 2016, vol. 170, issue 3, No 8, 838-852

Abstract: Abstract 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.

Keywords: Nonlinear programming; Hahn–Banach theorem; Separation theorem; Lagrange multipliers; Karush/Kuhn–Tucker theorem; Fritz John theorem; Infsup-convexity; 90C30; 46A22; 90C46; 26B25 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-016-0959-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:170:y:2016:i:3:d:10.1007_s10957-016-0959-1

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-016-0959-1

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().