Some Optimality Conditions Of ?-Strictly Efficient Solutions And Weakly Efficient Solutions

When ordered pair mapping consisting of the object function and constrained function is nearly cone-subconvexlike,under the assumption of weaker constraint qualification,with the help of separated theorem for convex sets,Lagrangian type optimality conditions for ?-strictly efficient solutions of set-valued optimization are obtained.The?-strict efficiency for set-valued optimization is discussed in Banach spaces.By virtue of the several prederivatives introduced by Ioffe etc,under the existence of prederivatives of set-valued mappings,necessary and sufficient optimality conditions for ?-strictly efficient solutions of set-valued optimization are obtained.When both the objective function and constrained function are M-derivative,under the assumption of nearly cone-subconvexlikeness,with the help of separated theorem for convex sets,necessary and sufficient optimality conditions are obtained for a point pair to be a weakly efficient element of vector equilibrium optimization problem with constraints.