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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Vydané v:Computers & mathematics with applications (1987) Ročník 53; číslo 1; s. 21 - 27
Hlavní autori: Zheng, Xiaojin, Xu, Zengkun, Li, Cheng
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Ltd 2007
Predmet:
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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Abstract 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.
AbstractList 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 super(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.
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 , 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.
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.
Author Xu, Zengkun
Li, Cheng
Zheng, Xiaojin
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Cites_doi 10.1006/jmaa.1998.6204
10.1016/j.jmaa.2003.10.041
10.1016/0022-247X(74)90289-3
10.1016/0022-247X(84)90090-8
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Issue 1
Keywords Nondifferentiable problems
Necessary optimality conditions
Fractional programming
Generalized gradient
Constraint qualifications
Language English
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Snippet The Kuhn–Tucker type necessary optimality conditions are given for the problem of minimizing a local Lipschitzian function subject to a set of differentiable...
The Kuhn-Tucker type necessary optimality conditions are given for the problem of minimizing a local Lipschitzian function subject to a set of differentiable...
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SubjectTerms Constraint qualifications
Fractional programming
Generalized gradient
Inequalities
Mathematical analysis
Mathematical models
Mathematical programming
Necessary optimality conditions
Nondifferentiable problems
Nonlinearity
Optimization
Quotients
Title Constraint qualification in a general class of nondifferentiable mathematical programming problems
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