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Duality theorems for a new class of multitime multiobjective variational problems

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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.

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Authors and Affiliations

  1. University “Politehnica” of Bucharest, Faculty of Applied Sciences, Splaiul Independenţei 313, 060042, Bucharest, Romania

    Ariana Pitea & Mihai Postolache

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  1. Ariana Pitea
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  2. Mihai Postolache
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Correspondence to Mihai Postolache.

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Pitea, A., Postolache, M. Duality theorems for a new class of multitime multiobjective variational problems. J Glob Optim 54, 47–58 (2012). https://doi.org/10.1007/s10898-011-9740-z

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  • DOI: https://doi.org/10.1007/s10898-011-9740-z

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