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

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Generalized Convexity and Related Topics

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 583))

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.

This research for the second and third authors was partially supported by Ministerio de Ciencia y Tecnología (Spain), project BMF2003-02194. The authors are grateful to the referee for his comments.

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Authors and Affiliations

  1. Dipartimento di Ricerche Aziendali, Università degli Studi di Pavia, Via S. Felice, 5, 27100, Pavia, Italy

    Giorgio Giorgi

  2. Departamento de Matemática Aplicada, E.T.S.I. Industriales, Universidad Nacional de Educación a Distancia, c/ Juan del Rosal, 12, Ciudad Universitaria, 28040, Madrid, Spain

    Bienvenido Jiménez & Vicente Novo

Authors
  1. Giorgio Giorgi
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  2. Bienvenido Jiménez
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  3. Vicente Novo
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Giorgi, G., Jiménez, B., Novo, V. (2007). Sufficient Optimality Conditions and Duality in Nonsmooth Multiobjective Optimization Problems under Generalized Convexity. In: Generalized Convexity and Related Topics. Lecture Notes in Economics and Mathematical Systems, vol 583. Springer, Berlin, Heidelberg . https://doi.org/10.1007/978-3-540-37007-9_15

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