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.

Finally,a conclusion is reached that our stock market has come into the weak efficiency stage.

This paper establishes one kind of constructions for vector Lagrangian functionals in a class of multiobjective fractional optimal control problems, called generalized Lagrangian functionals, and the relationship between the weak efficiency and generalized weak saddle points of such a kind of generalized Lagrangian functionals is discussed.

The result of an empirical study shows that in the aspect of industry, Chinese stocks market is neutral and is not weak efficiency.

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.

Some Sufficient Conditions of Weakly Efficient Solutions for Vector Optimization Problems with Cone Constrain;

In this weak topology case, we research the stability of the weakly efficient solutions of a kind of general meanings n-dimensioned vector-valued functionals.

It is very important to get all of the weakly efficient solutions of a multiobjective programming,be-cause a multiobjective programming has usually more than one weakly effi cient solution.