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Abstract and Applied Analysis
Volume 2012, Article ID 589694, 18 pages
http://dx.doi.org/10.1155/2012/589694
Research Article

Duality for Multitime Multiobjective Ratio Variational Problems on First Order Jet Bundle

Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independenţei, No. 313, 060042 Bucharest, Romania

Received 27 April 2012; Accepted 29 June 2012

Academic Editor: Allan Peterson

Copyright © 2012 Mihai Postolache. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider a new class of multitime multiobjective variational problems of minimizing a vector of quotients of functionals of curvilinear integral type. Based on the efficiency conditions for multitime multiobjective ratio variational problems, we introduce a ratio dual of generalized Mond-Weir-Zalmai type, and under some assumptions of generalized convexity, duality theorems are stated. We prove our weak duality theorem for efficient solutions, showing that the value of the objective function of the primal cannot exceed the value of the dual. Direct and converse duality theorems are stated, underlying the connections between the values of the objective functions of the primal and dual programs. As special cases, duality results of Mond-Weir-Zalmai type for a multitime multiobjective variational problem are obtained. This work further develops our studies in (Pitea and Postolache (2011)).