向量优化问题有效解的稳定性

THE STABILITY OF THE EFFICIENT SOLUTIONS FOR OPTIMIZATION PROBLEMS

运用标量化的方法,通过锥正定真有效解的上半连续性讨论了无限维赋范空间中锥有效解的部分上半连续性,证明了锥有效解的通有稳定性.在此基础上,进一步证明,在Baire纲的意义下,绝大多数的向量优化问题至少存在一个锥正定真有效解是本质的有效解,换句话说,绝大多数的向量优化问题锥有效解是几乎下半连续的.

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..