Abstract
We introduce a pair of second order mixed symmetric dual problems. Weak, strong and converse duality theorems for this pair are established under $F-$convexity assumptions.
Highlights
Dorn [5] introduced symmetric dual for quadratic programming problems
Symmetric duality for nonlinear programming has been studied by many researchers [4, 9, 11]
Ahmad and Husain [2] and Kailey et al [6] discussed a pair of multiobjective mixed symmetric dual programs over arbitrary cones and established duality results under K−preinvexity/K−pseudoinvexity and η−bonvexity/η−pseudobonvexity assumptions respectively
Summary
Symmetric duality for nonlinear programming has been studied by many researchers [4, 9, 11]. Mangasarian [8] considered a nonlinear program and discussed second order duality under certain inequalities. Bector et al [3] introduced mixed symmetric dual models for a class of nonlinear multiobjective programming problems. Ahmad [1] studied invexity/generalized invexity for mixed type symmetric dual in multiobjective programming problems ignoring nonnegativity constraints of Bector et al [3]. Ahmad and Husain [2] and Kailey et al [6] discussed a pair of multiobjective mixed symmetric dual programs over arbitrary cones and established duality results under K−preinvexity/K−pseudoinvexity and η−bonvexity/η−pseudobonvexity assumptions respectively. Strong and converse duality theorems for this pair are established under F −convexity assumptions
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