Journal of Convex Analysis 09 (2002), No. 1, 097--116
Copyright Heldermann Verlag 2002
Alternative Theorems and Necessary Optimality Conditions for Directionally Differentiable Multiobjective Programs
B. Jiménez
Dep. de Matemática Aplicada, Universidad Nacional de Educación a Distancia, Apartado 60149, 28080 Madrid, Spain
bjimen1@encina.pntic.mec.es
V. Novo
Dep. de Matemática Aplicada, Universidad Nacional de Educación a Distancia, Apartado 60149, 28080 Madrid, Spain
vnovo@ind.uned.es
We study, in a unified way, some alternative theorems that involve linear and sublinear functions between finite dimensional spaces and a convex set, and we propose several generalizations of them. These theorems are applied to obtain, under different constraint qualifications, several necessary conditions for a point to be Pareto optimum, both Fritz John and Kuhn-Tucker type, in multiobjective programming problems which are defined by directionally differentiable functions and which include three types of constraints: inequality, equality and set constraints. In particular, these necessary conditions are applicable to convex programs and to differentiable programs.
Keywords: Multiobjective programming, alternative theorems, necessary conditions for Pareto minimum, Lagrange multipliers.
MSC: 90C29; 90C46
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