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

In: Generalized Convexity and Related Topics

Author

Listed:
  • Giorgio Giorgi

    (Università degli Studi di Pavia)

  • Bienvenido Jiménez

    (Universidad Nacional de Educación a Distancia)

  • Vicente Novo

    (Universidad Nacional de Educación a Distancia)

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.

Suggested Citation

  • Giorgio Giorgi & Bienvenido Jiménez & Vicente Novo, 2007. "Sufficient Optimality Conditions and Duality in Nonsmooth Multiobjective Optimization Problems under Generalized Convexity," Lecture Notes in Economics and Mathematical Systems, in: Generalized Convexity and Related Topics, pages 265-278, Springer.
    • Handle: RePEc:spr:lnechp:978-3-540-37007-9_15
    DOI: 10.1007/978-3-540-37007-9_15
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    Cited by:

    1. Elena Constantin, 2019. "Necessary conditions for weak efficiency for nonsmooth degenerate multiobjective optimization problems," Journal of Global Optimization, Springer, vol. 75(1), pages 111-129, September.

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