Φ strict Local Efficient Solution for Multiobjective Programming Problems

The article generalizes the strict efficient solution of multiobjective programming problem (MOP) to Φ strict local efficient solution concept，thus pertains to characterize Φ strict local efficient solution for multiobjective programming problems (MOP) with inequality constraints.To create the necessary framework，we partition the index set of objective of MOP to give rise to subproblem (RMOPJB((P<α,δJB((xJB)),xTX-0.5mmJB))).The Φstrict local efficient solution (Φsles) for MOP is related to the local efficient solution of a subproblem (RMOPJB((P<α,δJB((xJB)),xTX-0.5mmJB)))，having lesser number of objective functions，with MOP.This paper will discuss their relationship.We will through the theorem discuss their relationship.We also generalize the strong convex function；put forward a new concept of convex function —Φstrongly convex function，and by the strong convex function and KKT conditions to characterize Φstrict local efficient solution for MOP.