Geodesic
Mixed Type Symmetric and Self Duality for Multiobjective Variational Problems With Support Functions
Yugoslav journal of operations research, Tome 23 (2013) no. 3, p. 387 .

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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.
Classification : 90C30, 90C11, 90C20, 90C26.
Keywords: Efficiency, mixed type symmetric duality, mixed type self duality, natural boundary values, multiobjective nonlinear programming, convexity-convexity, pseudoconvexity-pseudoconcavity, support functions. 
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     author = {I. Husain and Rumena Mattoo},
     title = {Mixed {Type} {Symmetric} and {Self} {Duality} for {Multiobjective} {Variational} {Problems} {With} {Support} {Functions}},
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I. Husain; Rumena Mattoo. Mixed Type Symmetric and Self Duality for Multiobjective Variational Problems With Support Functions. Yugoslav journal of operations research, Tome 23 (2013) no. 3, p. 387 . http://geodesic.mathdoc.fr/item/YJOR_2013_23_3_a5/