Sufficient Optimality Conditions and Duality in Nonsmooth Multiobjective Optimization Problems under Generalized Convexity

Giorgio Giorgi (), Bienvenido Jiménez () and Vicente Novo ()
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Giorgio Giorgi: Università degli Studi di Pavia
Bienvenido Jiménez: Universidad Nacional de Educación a Distancia
Vicente Novo: Universidad Nacional de Educación a Distancia

A chapter in Generalized Convexity and Related Topics, 2007, pp 265-278 from Springer

Abstract: Summary We consider a multiobjective optimization problem in ℝn with a feasible set defined by inequality and equality constraints and a set constraint. All the involved functions are, at least, directionally differentiable. We provide sufficient optimality conditions for global and local Pareto minimum under several kinds of generalized convexity. Also Wolfe-type and Mond-Weir-type dual problems are considered, and weak and strong duality theorems are proved.

Keywords: Multiobjective optimization problems; sufficient conditions for a Pareto minimum; Lagrange multipliers; tangent cone; quasiconvexity; Dini differentiable functions; Hadamard differentiable functions; duality theorems (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/978-3-540-37007-9_15

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