Algorithm Of Non - Smooth Equation And Its Application

Nonsmooth equations problem is a class of optimization problems which is closely related to the complementarity problems, variational inequality problem, engineering mechanics, financial analysis and many other optimization problems. The study of nonsmooth equations problems include theory research and algorithm design.The first chapter of this paper considers solving the nonsmooth equations with finitely many maximum functions, gives the steepest descent method and smoothing gradient method to solve the nonsmooth equations. In addition, we also give the convergence analysis of the method and the application in solving the generalized complementarity problem and the minimax optimization problem. Finally, the numerical experiments show that the smoothing gradient method is effectiveness in practical application.This second chapter of this paper continues to study the minimax nonsmooth problem which is widely applied in the fields of economic management and engineering technology. We also give a smoothing Fletcher-Reeves conjugate gradient method. Under general conditions, we prove the global convergence of the method and give the relevant numerical experiments.In the last part of the paper, we introduce the Newton type method for solving constraint nonsmooth equations. This method is put forward by Facc hinei F, it is a method using linear programming model to solve the constraint nonsmooth equations. Combined with the feature of the method, we give the application of the method in solving the constrained nonsmooth equations with finitely many maximum functions and the constrained generalized complementarity problems.