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.

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.

The author has proved Fritz John conditions and Kuhn-Tucker conditions ofα-major optimal constraint solutions on the bases of the representation ofα-major constraint structure set for the problem.

In this algorithm,inequality constrained least-square problems are first translated to convex quadratic programming problems and then translated to the linear complementarity problem(LCP) using Kuhn-Tucker conditions of quadratic programming,which consequently gives the general form of least-squares estimation in adjustment model,as well as the algorithm is simple and easy to understand.

On the Kuhn-Tucker sufficient conditions for a class of nonsmooth generalized Fractional multiobjective programming;