Abstract and Applied Analysis

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

Mihai Postolache

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)).

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 589694, 18 pages.

Dates
First available in Project Euclid: 14 December 2012

https://projecteuclid.org/euclid.aaa/1355495829

Digital Object Identifier
doi:10.1155/2012/589694

Mathematical Reviews number (MathSciNet)
MR2965448

Zentralblatt MATH identifier
1251.49043

Citation

Postolache, Mihai. Duality for Multitime Multiobjective Ratio Variational Problems on First Order Jet Bundle. Abstr. Appl. Anal. 2012 (2012), Article ID 589694, 18 pages. doi:10.1155/2012/589694. https://projecteuclid.org/euclid.aaa/1355495829

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