同伦方法求解无界域上非凸规划问题的收敛性定理

Convergence Theorems of Homotopy Method for Nonconvex Programming in Unbounded Set

利用同伦方法求解非凸规划时,一般只能得到问题的K-K-T点.本文得到无界域上同伦方法求解非凸规划的几个收敛性定理,证明在一定条件下,通过构造合适的同伦方程,同伦算法收敛到问题的局部最优解.

Generally, for nonconvex pogramming,we only get a K-K-T point from homo- topy method. In this paper,some convergence theorems of homotopy method for nonconvex programming in unbounded set are obtained. It is proved that, under suitable conditions, we can get a local optimal solution from the homotopy method by constructing proper homotopy equation.