scholarly journals Proper efficiency and duality for a new class of nonconvex multitime multiobjective variational problems

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Ariana Pitea ◽  
Tadeusz Antczak
Keyword(s):  
Variational Problems ◽  
Proper Efficiency ◽  
New Class ◽  
Multiobjective Variational Problems

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

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Mihai Postolache
Keyword(s):  
Variational Problems ◽  
Efficient Solutions ◽  
Integral Type ◽  
Duality Theorems ◽  
Jet Bundle ◽  
New Class ◽  
Special Cases ◽  
Multiobjective Variational Problems ◽  
Curvilinear Integral ◽  
Primal And Dual

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)).

scholarly journals Optimality Conditions and Duality for Multiobjective Variational Problems with Generalized -B-Type-I Functions

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
C. Nahak ◽  
N. Behera
Keyword(s):  
Optimality Conditions ◽  
Variational Problems ◽  
Sufficient Optimality Conditions ◽  
Type I ◽  
Duality Results ◽  
Multiobjective Variational Problems ◽  
Generalized Type

We use -type-I and generalized -type-I functions to establish sufficient optimality conditions and duality results for multiobjective variational problems. Some of the related problems are also discussed.

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