一类非凸规划K-K-T点的性质及同伦方法收敛定理

Property of the K-K-T Point and Convergence Theorem of Homotopy Method for a Class of Nonconvex Programming

对于目标函数为凸的一类非凸规划,证明了其K-K-T点一定是局部极小点。在求解此类非凸规划时,基于可行域满足较法锥条件更弱的拟法锥、弱拟法锥等条件下,同伦方法得到的K-K-T点一定是局部极小点。对于一般非凸规划问题,证明了边界上的K-K-T点如果不是驻点,则一定是局部极小点。

It is proved that, the K-K-T point of a class of nonconvex programming problem, objective function of which is convex, is a local minimum. For this nonconvex programming problem under the quasi-normal cone condition or the weak quasi-normal cone condition, which are weaker than normal,cone condition the K-K-T point got by homotopy method must be a lo- cal minimum.It is also proved that,for general nonconvex programming problem,if the K-K-T point on the boundary is not a stationary point,it must be a local minimum.