scholarly journals Mixed Type Duality for Multiobjective Variational Problems

2000 ◽  
Vol 252 (2) ◽  
pp. 571-586 ◽  
Author(s):  
R.N Mukherjee ◽  
Ch.Purnachandra Rao
Keyword(s):  
Mixed Type ◽  
Variational Problems ◽  
Multiobjective Variational Problems ◽  
Mixed Type Duality

scholarly journals Mixed type symmetric and self duality for multiobjective variational problems with support functions

2013 ◽  
Vol 23 (3) ◽  
pp. 387-417
Author(s):  
I. Husain ◽  
Rumana Mattoo
Keyword(s):  
Mixed Type ◽  
Variational Problems ◽  
Kernel Functions ◽  
Boundary Values ◽  
Natural Boundary ◽  
Duality Theorems ◽  
Support Functions ◽  
Self Duality ◽  
Multiobjective Nonlinear Programming ◽  
Multiobjective Variational Problems

In this paper, a pair of mixed type symmetric dual multiobjective variational problems containing support functions is formulated. This mixed formulation unifies two existing pairs Wolfe and Mond-Weir type symmetric dual multiobjective variational problems containing support functions. For this pair of mixed type nondifferentiable multiobjective variational problems, various duality theorems are established under convexity-concavity and pseudoconvexity-pseudoconcavity of certain combination of functionals appearing in the formulation. A self duality theorem under additional assumptions on the kernel functions that occur in the problems is validated. A pair of mixed type nondifferentiable multiobjective variational problem with natural boundary values is also formulated to investigate various duality theorems. It is also pointed that our duality theorems can be viewed as dynamic generalizations of the corresponding (static) symmetric and self duality of multiobjective nonlinear programming with support functions.

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