Constraint qualifications in a class of nondifferentiable mathematical programming problems

The Kuhn–Tucker type necessary optimality conditions are given for the problem of minimizing the sum of a differentiable function and a convex function subject to a set of differentiable nonlinear inequalities on a convex subset C of R n , under the conditions similar to the Kuhn–Tucker constraint q...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 302; no. 2; pp. 282 - 290
Main Author: Xu, Zengkun
Format: Journal Article
Language:English
Published: San Diego, CA Elsevier Inc 15.02.2005
Elsevier
Subjects:
Calculus of variations and optimal control
Constraint qualifications
Exact sciences and technology
Mathematical analysis
Mathematics
Necessary conditions
Nondifferentiable problems
Sciences and techniques of general use
Nondifferentiable problems
Constraint qualifications
Necessary conditions
Necessary condition
Constraint qualification
Non differentiable programming
Mathematical analysis
Optimality condition
Convex function
Mathematical programming
ISSN:0022-247X, 1096-0813
Online Access:Get full text
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Summary:The Kuhn–Tucker type necessary optimality conditions are given for the problem of minimizing the sum of a differentiable function and a convex function subject to a set of differentiable nonlinear inequalities on a convex subset C of R n , under the conditions similar to the Kuhn–Tucker constraint qualification or the Arrow–Hurwicz–Uzawa constraint qualification. The case when the set C is open (not necessarily convex) is shown to be a special one of our results, which helps us to improve some of the existing results in the literature.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2003.10.041