Mixed type symmetric duality for multiobjective variational problems with cone constraints

2013 ◽  
Vol 21 (2) ◽  
pp. 291-310 ◽  
Author(s):  
I. Ahmad ◽  
Z. Husain ◽  
S. Al-Homidan
Keyword(s):  
Mixed Type ◽  
Variational Problems ◽  
Symmetric Duality ◽  
Cone Constraints ◽  
Multiobjective Variational Problems

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.

scholarly journals Second-order symmetric duality in multiobjective variational problems

2019 ◽  
Vol 29 (3) ◽  
pp. 295-308
Author(s):  
Geeta Sachdev ◽  
Khushboo Verma ◽  
T.R. Gulati
Keyword(s):  
Variational Problems ◽  
Second Order ◽  
Static Case ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Converse Duality ◽  
Multiobjective Variational Problems ◽  
Second Order Symmetric Duality

In this work, we introduce a pair of multiobjective second-order symmetric dual variational problems. Weak, strong, and converse duality theorems for this pair are established under the assumption of ?-bonvexity/?-pseudobonvexity. At the end, the static case of our problems has also been discussed.

scholarly journals Second order symmetric duality in fractional variational problems over cone constraints

2018 ◽  
Vol 28 (1) ◽  
pp. 39-57
Author(s):  
Anurag Jayswal ◽  
Shalini Jha
Keyword(s):  
Duality Theorem ◽  
Variational Problems ◽  
Second Order ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Self Duality ◽  
Cone Constraints ◽  
Fractional Variational Problems ◽  
Second Order Symmetric Duality ◽  
Convexity Assumptions

In the present paper, we introduce a pair of second order fractional symmetric variational programs over cone constraints and derive weak, strong, and converse duality theorems under second order F-convexity assumptions. Moreover, self duality theorem is also discussed. Our results give natural unification and extension of some previously known results in the literature.

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