Constraint qualification in a general class of nondifferentiable mathematical programming problems

The Kuhn–Tucker type necessary optimality conditions are given for the problem of minimizing a local Lipschitzian function subject to a set of differentiable nonlinear inequalities on a convex subset C of R n , under the conditions of the generalized Kuhn–Tucker constraint qualification or the gener...

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Veröffentlicht in:Computers & mathematics with applications (1987) Jg. 53; H. 1; S. 21 - 27
Hauptverfasser: Zheng, Xiaojin, Xu, Zengkun, Li, Cheng
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 2007
Schlagworte:
Constraint qualifications
Fractional programming
Generalized gradient
Inequalities
Mathematical analysis
Mathematical models
Mathematical programming
Necessary optimality conditions
Nondifferentiable problems
Nonlinearity
Optimization
Quotients
Nondifferentiable problems
Necessary optimality conditions
Fractional programming
Generalized gradient
Constraint qualifications
ISSN:0898-1221, 1873-7668
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Zusammenfassung:The Kuhn–Tucker type necessary optimality conditions are given for the problem of minimizing a local Lipschitzian function subject to a set of differentiable nonlinear inequalities on a convex subset C of R n , under the conditions of the generalized Kuhn–Tucker constraint qualification or the generalized Arrow–Hurwicz–Uzawa constraint qualification. The case when the set C is open is shown to be a special one of our results, which helps us to improve some of the existing results in the literature. What’s more, the case when the object function is the sum of a differentiable function and a convex function is also the special case of our results. Finally, the case when the object function is the quotient of two Lipschitz functions is the special case of our results too.
Bibliographie:ObjectType-Article-2
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2006.05.018