Journal of Global Optimization

, Volume 54, Issue 1, pp 47–58

Duality theorems for a new class of multitime multiobjective variational problems

Article

DOI: 10.1007/s10898-011-9740-z

Cite this article as:
Pitea, A. & Postolache, M. J Glob Optim (2012) 54: 47. doi:10.1007/s10898-011-9740-z

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 problemEfficient solutionQuasiinvexityDuality

Mathematics Subject Classification (2000)

65K1090C29 26B2526B25

Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

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