Mixed Duality for Programming with Semi-r-preinvexity Functions

In this paper, we introduced a new class of generalized convex function, called semi-r-preinvex function, which generalized r-preinvex function and semi-preinvex function. We investigated mixed type duality involving semi-r-preinvex function. Firstly, a characterization about differentiable semi-r-preinvex function is presented; secondly, we established dual model of a class of multiobjective programming involving differentiable constraint and objective function and proved the corresponded weak duality, strong duality and strictly inverse duality, which generalized the corresponded result of preinvex function, r-preinvex function and semi-preinvex function.