The Saddle Point Research Of Multi Objective Programming Under Generalized Convexity

People in the political, economic and daily life often need to make decisions. To make good decisions, first need to give a criteria to determine good or bad decisions. How to reconcile these contradictions, take into account the various indicators, and choose the most satisfied sloution is the problem that people often encounter in real life, so multi-objective planning do it. Further, saddle-point is the most attractive theme that many scholars researched in multi-objective planning optimization theory, especially the saddle-point can ensure the existence of the overall optimal solution in multi-objective planning. And many meaningful and important results in the optimization theory was base on the the convex and some assumptions on the convexity. In this paper, we stand on the basis of previous research which weaken the conditions of multi-objective planning,get the concept and some meanful theorems of semi-convexlike unchang function and subconvexlike function,which in chapters III and IV to Research from the MP problem to VFP problem, obtain the existence of saddle in semi-convexlike unchang function and subconvexlike function under the weaken situation.