一般约束极大极小值的梯度投影算法

A Projection Gradient Method for General Max-min Problem

对一类带等式、不等式约束的极大极小值问题进行了研究,将其转化为带等式、不等式约束的非线性规划问题,并利用梯度投影算法进行求解。该算法在有限步达到最优点或产生一系列点,且其极限点是最优点。该算法减少了计算量,克服了数值实现上的困难,证明了算法的收敛性。

In this paper, a max-min problem with inequality and equality constraints is studied and made into nonlinear optimization problem with inequality and equality. Gradient projcet method is also given. The algorithms get optimization point in infinite steps or get a series of points, whose limit points are optimization points. The algorithms save lots of calculating time and overcome some difficulties in computation, whose convergence are also proved.