The Theory And Algorithm Research Of Absolute Value Equation Problem

The absolute value equations is a kind of important nonsmooth problem.It is widely used in many fileds,such as economic equilibrium filed.In recent years,the theory and methods for the absolute value equations have been developed greatly.In this thesis,we study the theory and methods for solving absolute value equations.The structure and main contents of this thesis are summarized as follows:In the first chapter,the basic situation of absolute value equations is introduced and the significance,the conditions of the solutions and some applications of absolute value equations are also given.In the second chapter,the method for solving absolute value equations with inexact linesearch is studied.Under the conditions of Wolfe type linesearch and Armijo type linesearch,the Levenberg-Marquardt method for absolute value equations is proposed.And under the general assumptions,the global convergence of the Levenberg-Marquardt method is also given.Finally,the related numerical results indicate that the given method is efficientive.In the third chapter,the method for solving a kind of generalized absolute value equations is studied.By auxiliary function,the equivalent form of the generalized absolute value equations is given.The conjugate gradient method for this equivalent problem is also proposed.And under general assumptions,the global convergence of the conjugate gradient method is given.Finally,the related numerical results indicate that the given method is efficientive.In the fourth chapter,a kind of symmetrical tensor absolute value equations is studied.And the nonsmooth Newton method is proposed.Under general assumptions,the local convergence of the method is given.Finally,the related numerical results indicate the efficiency of the method.