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A pair of higher order symmetric non differentiable minimax mixed programming problem where each objective function contains support function of compact convex set in Rn, is formulated. Under higher order F-convexity assumption, weak, strong and converse symmetric duality theorems related to a properly efficient solution and self-duality are proved. Symmetric duality in nonlinear programming problem was first introduced by Dorn who defined a mathematical programming problem and it's dual to be symmetric if the dual is the primal problems.
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