Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Multiobjective programming
  • alternative theorems
  • necessary conditions for Pareto minimum
  • Lagrange multipliers

Mathematics Subject Classification

90C29; 90C46

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Suggested citation

B. Jiménez, V. Novo. “Alternative Theorems and Necessary Optimality Conditions for Directionally Differentiable Multiobjective Programs.” Journal of Convex Analysis 9 (2002), No. 1, 97–116. https://doi.org/10.68381/jca09005

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Published by Heldermann Verlag, 2002. Rights now held by Banach Press LLC.