Numerical Algorithm Of Maximum Value Equation And Its Application Research

The nonsmooth equations with finitely many maximum functions is a kind of important problem of the nonsmooth equations.It is often used for the research of nonlinear complementarity problems,variational inequality problems and engineering mechanics problems,and is widely used in image storage,variable selection,the stochastic equilibrium and optimal control.In this paper,we mainly study the algorithm and the applications of the nonsmooth equations with finitely many maximum functions.In the first chapter,we give the brife introduce of the knowledge of the nonsmooth equations with finitely many maximum functions,including the source of the problem,the development situation and etc.,and also give the introduce of the applications of the nonsmooth equations with finitely many maximum functions.In the second chapter,the parameterized combinations Newton method for solving the nonsmooth equations with finitely many maximum functions is considered.A new differential is used in the given Newton-type method.The local superlinear convergence of the given methods are presented under the general assumption condition.The relevant numerical experiments show that the method is effective.In the third chapter,the modified parameterized combinations Newton method for solving the nonsmooth equations with finitely many maximum functions is given.This method overcome the limitation of the requirements of non-singular ofkV.The local superlinear convergence is proved and the numerical experiments are also given.In the fourth chapter,we put a kind of general complementarity problem transformed into the nonsmooth equations with finitely many maximum functions,and use the given parameterized combinations Newton methods to solve it.