In ordered linear spaces,generalized vector Fritz-John saddle point and generalized vector Kuhn-Tucker saddle point of set-valued optimization problems with generalized inequality constraints were defined,and the relations between them were established.

In the framework of locally convex topological vector space,the scalarization theorem,Kuhn-Tucker conditions as well as the duality theorem and the saddle points theorem on Henig proper efficient solutions with respect to the base for vector optimization involving arcwise connected convex maps are established separately.

In our algorithm,replacing the lower level problem by its Kuhn-Tucker condition,the bilevel linear programming is transformed into a traditional single-level programming problem,which can be transformed into a series of linear programming problem.

Via connecting linear plus power module ideal point algorithm under Kuhn-Tucker condition,the bilevel multiobjective programming problem is changed to a singula.

One computing method of the minimizing internal forces in multiple robot manipulating systems based on the Kuhn-Tucker theorem was proposed because the Kuhn-Tucker theorem can transform the complex restricted conditions of the minimizing extremism problem.

In this paper, using a saddle point theorem we prove an abstract Kuhn-Tucker theorem, in which we give an equivalent condition on the existence of solutions of nonlinear programming problems for abstract functions with constrains in operator form.

As for weak efficient solution to multi objective programming inequality and equality constrants, the new necessary condition between Fritz John condition and Kuhn Tucker condition is established under weaker condition.