Abstract: 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.