The Numerical Methods For Minimax Problem

The Minimax problem is an important nondifferetiable optimization problem.lt finds many application from project design to electric circuit problem as well as game theory.And the problem has relation with several standard problems,such as nonlinear equations,nonlinear inequalities,nonlinear program and multiobjective program.lt is well known in recent years.The paper study the advantages and disadvantages of the past,and three methods are proposed.Details are as follows:Firstly,some new extension of the generalized gradient method is discussed. Used perturbed method and making inexact generalized gradient projection with cone, perturbed generalized gradient projection method is proposed.The field of the algorithm is extended.Numerical experiments show that the method is effective.Secondly,using the trust region form and the pseudo-directional derivative of minimax problem,we propose the trust region form of minimax problem. Then nonmonotone trust region algorithm is given and global convergence is proved.Thirdly, based on complementary conditions and NCP theory, the minimax problem is transformed into nonsmooth equation.we introduce an numerical algorithm relating with splitting function method.