Optimality Conditions And Duality For Generalized Arcwise-Connected Functions

In this paper, the arc wise-connected and generalized arcwise-connected functions, defined on the AC set S Rn, are introduced. They are new classes of generalized convex functions. Functions belonging to these classes satisfy certain local-global minimum properties. Conversely, it is shown that, under some mild regularity conditions, functions for which the local-global minimum properties hold must belong to one of the classed of the functions introduced. Furthermore, under the hypothesis of generalized convexity, the sufficient optimality conditions of problem min f(x),s.t.g(x) < 0 are studied. Then the weak and strong duality theoryare derived for the duality problem.