A finite dimensional extension of Lyusternik theorem with applications to multiobjective optimization

We consider a multiobjective program with inequality and equality constraints and a set constraint. The equality constraints are Fréchet differentiable and the objective function and the inequality constraints are locally Lipschitz. Within this context, a Lyusternik type theorem is extended, establi...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2002-06, Vol.270 (2), p.340-356
Main Authors: Jiménez, Bienvenido, Novo, Vicente
Format: Article
Language:English
Subjects:
Applied sciences
Calculus of variations and optimal control
Clarke derivative
Exact sciences and technology
Lagrange multipliers
Mathematical analysis
Mathematical programming
Mathematics
Multiobjective optimization
Necessary optimality conditions
Nonsmooth analysis
Operational research and scientific management
Operational research. Management science
Sciences and techniques of general use
Tangent cone
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Summary:We consider a multiobjective program with inequality and equality constraints and a set constraint. The equality constraints are Fréchet differentiable and the objective function and the inequality constraints are locally Lipschitz. Within this context, a Lyusternik type theorem is extended, establishing afterwards both Fritz–John and Kuhn–Tucker necessary conditions for Pareto optimality.
ISSN:0022-247X
1096-0813
DOI:10.1016/S0022-247X(02)00064-1