一般约束极大极小问题的广义梯度投影算法

讨论了一类带等式、不等式约束的极大极小值问题,将其转化为带等式、不等式约束的非线性规划问题,利用辅助规划进行处理,给出了一个广义的梯度投影算法,解决了一般约束极大极小值问题。算法可在有限步达到最优点或产生一系列点列,其极限点则是最优点,并证明了该算法的全局收敛性。

A General Projection Gradient Method for General Max-min Problems

In this paper, a sort of max-min problems with inequality and equality are discussed,which are made into nolinear optimization problems with inequality and equality.Auxiliny problem and penality function are used to deal with max-min problems. A general projection gradient method is given,and the max-min problems with general constraints problems are solved. The algorithms get optimizaion point in infinite steps or get a series of points, whose limit points are optimization points. The algorithm convergence is also proved.