The weak duality theorem, the basic duality theorem, the direct duality theorem and the adverse duality theorem under the means of the joint weak efficient solution are derived.

For a group multiobjective programming problem, the stability results of a class of joint cone weakly efficient solution sets in the sense of upper semi-continuance were obtained with respect to the decision making variable perturbation and objective order perturbation respectively.

This paper is concerned with Mond-Weir type duality about the joint efficient solution in group multiobjective programming, which contains the unsymmetrical objective functions and constraints.

In [1], the concept of a class joint efficient solution to group multiobjective decision making problem is introduced, as well as some optimality necessary conditions for these solutions.

For group multiobjective decision making problems, a class of joint efficient solutions is introduced by means of efficient numbers of alternatives and the optimality necessary conditions are established in the paper [1].

Weak Efficient Solutions for Some Kinds of Vectorial Optimization Problems in Banach Spaces

This paper studied a class of multiobjective programing problems involving differentiable n-set functions,and obtained sufficient optimality conditions for weak efficient solutions under generalized convexity conditions.

The paper studied that weak efficient solutions are stable with set-valued maps in the topological structure and it is proved that the weak efficient solutions and weak efficient points are stable in the sense of Baire dimension.

A necessary condition of weak efficient solution to multi-objective programming;

Under the conditions of Partial ic-convexlike Maps,optimality necessary conditions of weak efficient solutions for vector optimization problems with equality and inequality constraints are obtained.

An optimal condition of the existence of weak efficient solution for B－ subpseudoconvex set－ valued map is constructed.