Journal of Convex Analysis 18 (2011), No. 3, 749--768
Copyright Heldermann Verlag 2011
Characterization of Weakly Efficient Solutions for Non-Regular Multiobjective Programming Problems with Inequality-Type Constraints
Beatriz Hernández-Jiménez
Depto Economía, Métodos Cuantitativos e Historia Económica, Area de Estadística e Investigación Operativa, Universidad Pablo de Olavide, Edificio 3 - Ctra Utrera - Km 1, 41013 Sevilla, Spain
mbherjim@upo.es
Marko A. Rojas-Medar
Departamento de Ciencias Básicas, Facultad de Ciencias, Universidad del Bío-Bío, Campus Fernando May, Chillán, Chile
marko@ueubiobio.cl
Rafaela Osuna-Gómez
Departamento de Estadística e Investigación Operativa, Facultad de Matemáticas, Universidad de Sevilla, Aptdo. 1160, 41012 Sevilla, Spain
rafaela@us.es
Antonio Rufián-Lizana
Departamento de Estadística e Investigación Operativa, Facultad de Matemáticas, Universidad de Sevilla, Aptdo. 1160, 41012 Sevilla, Spain
rufian@us.es
Necessary conditions of optimality are presented for weakly efficient solutions to multiobjective minimization problems with inequality-type constraints. These conditions are applied when the constraints do not necessarily satisfy any regularity assumptions and they are based on the concept of 2-regularity introduced by Izmailov. In general, the optimality conditions do not provide the complete weak Pareto optimal set, so 2-KKT-pseudoinvex problems are defined. This new concept of generalized convexity is both necessary and sufficient to guarantee the characterization of all weakly efficient solutions based on the optimality conditions and it is the weakest one.
Keywords: Convexity, regularity, constraints qualifications, optimality conditions.
MSC: 90C29, 90C46, 26B25, 46T20, 47J20
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