同伦方法求解一类非凸规划问题的新的收敛性定理

A New Convergence Theorem of Homotopy Method for a Class of Nonconvex Programming

同伦方法求解非凸规划的收敛点只是问题的K-K-T点。对于目标函数为凸的一类非凸规划,得到了同伦方法求解的一个新的收敛性定理,证明了无论同伦映射是否为正则映射,同伦方法求得的K-K-T点一定是局部极小点。

For nonconvex programming problem,we only get a K-K-T point of the problem by homotopy method. For a class of nonconvex programming problems,objective function of which is convex,a new convergence theorem of homotopy method is obtained. It is proved that,whether the homotopy map is a regular map or not,the K-K-T point got by homotopy method is definitely a local minimum.