Infinite programming and theorems of the alternative

In this paper, we obtain optimal versions of the Karush–Kuhn–Tucker, Lagrange multiplier, and Fritz John theorems for a nonlinear infinite programming problem where both the number of equality and inequality constraints is arbitrary. To this end, we make use of a theorem of the alternative for a fam...

Full description

Saved in:
Bibliographic Details
Published inMathematical methods in the applied sciences Vol. 42; no. 17; pp. 5769 - 5778
Main Authors Montiel López, Pablo, Ruiz Galán, Manuel
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 30.11.2019
Subjects
Convexity
infsup‐convexity
Lagrange multiplier
Nonlinear programming
Theorems
theorems of the alternative
Online AccessGet full text
ISSN0170-4214
1099-1476
DOI10.1002/mma.5566

Cover

More Information
Summary:In this paper, we obtain optimal versions of the Karush–Kuhn–Tucker, Lagrange multiplier, and Fritz John theorems for a nonlinear infinite programming problem where both the number of equality and inequality constraints is arbitrary. To this end, we make use of a theorem of the alternative for a family of functions satisfying a certain type of weak convexity, the so‐called infsup‐convexity.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.5566