Research On Gradient Algorithms Of Maximum Value Function Equations

In this paper,the nonsmooth equations of a class of special max-type functions is studied.First,the smoothing function of the absolute value function and the smoothing function of the max-type function are used to smooth the nonsmooth equations.Then,smoothing gradient type methods for solving such problems are proposed and the global convergence analysis of the methods are also given.The structure of this thesis are summarized as follows:In the first chapter,based on the smoothing function of the absolute value function and the smoothing function of the max-type function,the smoothing spectral conjugate gradient method for solving the nonsmooth equations of a class of special max-type function problem is studied.Under general assumptions,the global convergence of the method is also given.Finally,the numerical experiments show the effectiveness of the proposed method.In the second chapter,the smoothing function of the absolute value function and the smoothing function of the max-type function are used to transform the nonsmooth equations.Based on the transformation problem,a smoothing Barzilai-Borwein scaling conjugate gradient method is given.The global convergence analysis and the corresponding numerical results are also given.In the third chapter,a smoothing cautious DPRP conjugate gradient method is proposed to solve the nonsmooth equations of a class of special max-type functions.Then the global convergence analysis of the method is given.Finally,the numerical results show the effectiveness of the method.