基于P序的参数集优化问题解的稳定性

Stability of solutions to parametric set optimization with possible less order relations

摘要:

Possible less序关系（P序）是一种相对较新的集序关系，在计算机编译器、区间运算以及鲁棒优化等方面均有应用.本文在P序下讨论了参数集优化问题解映射的稳定性.本文给出了P序关系下严格拟凸以及水平集映射的定义，得到了参数集优化问题解映射上下半连续性的充分条件，并给出了例子加以验证.

Abstract:

Possible less order relation is a new set order relation introduced by Chiriaev in interval arithmetic and it is implemented in Fortran compiler and robust optimization. In this paper, the stability of the solution mapping to parametric set optimization with possible less order relation is studied. Some sufficient conditions for the upper semicontinuity and lower semicontinuity of the solution mapping are given.