THE STABILITY OF THE EFFICIENT SOLUTIONS FOR OPTIMIZATION PROBLEMS

In terms of the method of scalar assignment,the partly upper semicontinuity of cone efficient solution in infinite dimensional normed spaces is investigated by using the upper semicontinuity of cone positive proper efficient solution,and the generic stability of cone efficient solution is proved.Then,in the sense of Baire catalogue,it is shown that for almost all optimization problems,there exists at least one cone positive proper efficient solution that is essential efficient solution.That is to say,for almost all optimization problems,a cone efficient solution is a.l.s.c..