一类张量绝对值方程问题的Levenberg-Marquardt算法

Levenberg-Marquardt Method for a Kind of Tensor Absolute Value Equations

研究一类张量绝对值方程问题的求解方法,并将此类张量绝对值方程问题转化为广义张量互补问题.基于Fischer-Burmeister函数,将转化的广义张量互补问题转化为非光滑方程问题.用Levenberg-Marquardt算法对转化的非光滑方程问题进行求解,并在一般的假设条件下给出算法的收敛性结果.数值实验结果表明算法的有效性.

The method for solving a kind of tensor absolute value equations was studied,and the problem was transformed into a generalized tensor complementarity problem.Based on the Fischer-Burmeister function,the transformed generalized tensor complementarity problem was transformed into the nonsmooth equations.Levenberg-Marquardt method was proposed to solve the transformed nonsmooth equations,and the convergence of the method was given under mild conditions.The numerical results show the efficiency of the method.