Multiplier Rules and Saddle-Point Theorems for Helbig's Approximate Solutions in Convex Pareto Problems

Authors:
César Gutiérrez;Bienvenido Jiménez;Vicente Novo
Affiliations:
Departamento de Matemática Aplicada, ETSII, Edificio de Tecnologías de la Información y las Telecomunicaciones, Universidad de Valladolid, Valladolid, Spain 47011;Departamento de Economía e Historia Económica, Facultad de Economía y Empresa, Universidad de Salamanca, Salamanca, Spain 37007;Departamento de Matemática Aplicada, ETSII, Universidad Nacional de Educación a Distancia, Madrid, Spain 28040
Venue:
Journal of Global Optimization
Year:
2005

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Abstract

This paper deals with approximate Pareto solutions in convex multiobjective optimization problems. We relate two approximate Pareto efficiency concepts: one is already classic and the other is due to Helbig. We obtain Fritz John and Kuhn---Tucker type necessary and sufficient conditions for Helbig's approximate solutions. An application we deduce saddle-point theorems corresponding to these solutions for two vector-valued Lagrangian functions.