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Duality and a Characterization of Pseudoinvexity for Pareto and Weak Pareto Solutions in Nondifferentiable Multiobjective Programming |
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| Authors: | M. Arana-Jiménez G. Ruiz-Garzón R. Osuna-Gómez B. Hernández-Jiménez |
| Affiliation: | 1. Departamento de Estadística e I.O., Facultad de Ciencias Sociales y de la Comunicación, Universidad de Cádiz, 11405, Jerez de la Frontera, Spain 2. Departamento de Estadística e I.O., Universidad de Sevilla, Sevilla, Spain 3. Departamento de Economía, Métodos Cuantitativos e H. Económica, Universidad Pablo de Olavide, Seville, Spain |
| Abstract: | In this paper, we unify recent optimality results under directional derivatives by the introduction of new pseudoinvex classes of functions, in relation to the study of Pareto and weak Pareto solutions for nondifferentiable multiobjective programming problems. We prove that in order for feasible solutions satisfying Fritz John conditions to be Pareto or weak Pareto solutions, it is necessary and sufficient that the nondifferentiable multiobjective problem functions belong to these classes of functions, which is illustrated by an example. We also study the dual problem and establish weak, strong, and converse duality results. |
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