Sufficiency and Duality for Multiobjective Programming under New Invexity

A class ofmultiobjective programming problems including inequality constraints is considered. To this aim, some new concepts of generalized (F, P)-type I and (F, P)-type II functions are introduced in the differentiable assumption by using the sublinear function F. These new functions are used to establish and prove the sufficient optimality conditions for weak efficiency or efficiency of the multiobjective programming problems. Moreover, two kinds of dual models are formulated. The weak dual, strong dual, and strict converse dual results are obtained under the aforesaid functions.