Research On Algorithm And Application Of Absolute Value Equation

In this thesis, we study the algorithms of solving the absolute value equations and its related applications. The convergence theorems of the algorithm and the corresponding numerical tests are given. And the related discussion of the algorithms are also presented.In the first chapter, the absolute value equations and its related properties are introduced. And the algorithms of solving the absolute value equations are also given.In the second chapter, firstly, the absolute value equations is transformed into an unconstrained optimization problem, and a smoothing gradient method is given to solve the absolute value equations by solving the unconstrained optimization problem. The convergence of the algorithm is also proved. Then, the validity of the algorithm is shown by numerical experiments.In the third chapter, by using the equivalence of the absolute value equations and the linear complementary problems, we give the successive algorithm to solve the linear complementarity problems. The numerical experiments show the effectiveness of the algorithm.The fourth chapter, we give the convergence analysis of the smoothing Levenberg-Marquardt method under the local error bound for nonlinear equations. And the method is also used to solve absolute value equations and linear complementarity problems. The related numerical experiments show the effectiveness of the algorithm.