Research On Iterative Algorithms Of Absolute Value Equations With Positive Definite Matrix

Absolute value equations is widely appear in optimization problems such as linear complementarity problem,quadratic programming,linear programming,constrain-ed minimization squares problem,and portfolio optimization problem etc.They are a class of optimization problems with a wide range of practical applications.Therefore,the study on absolute value equations has very important applications and theoretical values.This paper mainly studies the iterative algorithms and their convergence theory of the absolute value system Ax(10)B| x|(28)b,where A is a positive definite matrix and B is a Hermitian matrix.The specific research results are as follows:Firstly,the P-regular splitting iterative method of absolute value equations is proposed and the convergence theory is proved.Numerous numerical experiments show that this method is faster than the Picard-HSS method.Secondly,a double-splitting iterative method for the system of absolute value equations is proposed to prove its convergence theory.On this basis,an iterative method for solving an absolute value system with saddle-point matrix structure is proposed.Finally,numerical experiments show that the double-split iteration method is The conditions are better than the Picard-HSS method.Thirdly,a two-stage splitting iterative method for solving absolute value equations is proposed,and its convergence theory is proved.The comparison between numerical experiments and Picard-HSS method shows that the method is more effective under certain conditions.