Research On The Problem Of Tensor Absolute Value Equation

The tensor absolute value equations is a kind of important optimization problem.In recent years,with the study of tensor related problems in theory and methods,the research of tensor absolute value equations has made some progress.This paper mainly studies the theory and methods of tensor absolute value equations.The structure and main research contents of this paper are summarized as follows:In the first chapter,we introduce the form and basic situation of tensor absolute value equations and tensor complementarity problem.We also give the transformation of tensor value equations.In the second chapter,the Levenberg-Marquardt method for solving tensor absolute value equations is given.Based on the Fischer-Burmeister function,the transformed generalized tensor complementarity problem is transformed into the nonsmooth equations.The convergence analysis of the given method under the mild conditions is also given,and the numerical results show that the method is effective for solving tensor absolute value equations.In the third chapter,we give the smoothing spectral gradient method with Armijo line search for solving tensor absolute value equations.Under the mild conditions,the global convergence analysis of the given method is proposed,and the numerical experiments show that the proposed method is effective for solving tensor absolute value equations.