Multi-objective infinite programming

Authors:
Valeriano Antunes de Oliveira;Marko Antonio Rojas-Medar
Affiliations:
Departamento de Matemática Aplicada, Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas, CP 6065, CEP 13083-859, Campinas ...;Departamento de Ciencias Básicas, Facultad de Ciencias, Universidad del Bío-Bío, Campus Fernando May, Casilla 447, Chillán, Chile
Venue:
Computers & Mathematics with Applications
Year:
2008

Citing 3
Cited 1

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Journal of Optimization Theory and Applications
Optimality conditions for Pareto nonsmooth nonconvex programming in Banach spaces

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Preinvex functions and weak efficient solutions for some vectorial optimization problem in Banach spaces

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New optimality conditions for nonsmooth control problems

Journal of Global Optimization

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Abstract

Using the theory of abstract optimization problems in infinite-dimensional spaces we provide necessary optimality conditions of first and second order for weakly efficient solutions of the multi-objective infinite programming problem. Sufficient conditions are given under invexity assumptions. We generalize the notion of KKT-invexity for the multi-objective infinite problem and show that this notion is a necessary and sufficient condition for every vector KKT solution to be a weakly efficient solution. Moreover, we develop a theorem of the alternative, useful for proving some of our results.