Journal of Global Optimization

, Volume 54, Issue 1, pp 47–58 | Cite as

Duality theorems for a new class of multitime multiobjective variational problems

Article

Abstract

In this work, we consider a new class of multitime multiobjective variational problems of minimizing a vector of functionals of curvilinear integral type. Based on the normal efficiency conditions for multitime multiobjective variational problems, we study duals of Mond-Weir type, generalized Mond-Weir-Zalmai type and under some assumptions of (ρ, b)-quasiinvexity, duality theorems are stated. We give weak duality theorems, proving that the value of the objective function of the primal cannot exceed the value of the dual. Moreover, we study the connection between values of the objective functions of the primal and dual programs, in direct and converse duality theorems. While the results in §1 and §2 are introductory in nature, to the best of our knowledge, the results in §3 are new and they have not been reported in literature.

Keywords

Multitime multiobjective problem Efficient solution Quasiinvexity Duality 

Mathematics Subject Classification (2000)

65K10 90C29 26B25 26B25 

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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  1. 1.University “Politehnica” of Bucharest, Faculty of Applied SciencesBucharestRomania

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