A sufficient descent nonlinear conjugate gradient method for solving [formula omitted]-tensor equations

Abstract

Tensor equations is a kind of important tensor optimization problems with higher order nonlinear equations, which are widely used in engineering and economics. This paper is concerned with solving M-tensor equations. We transform M-tensor equations to nonlinear unconstrained optimization problems. Then, a sufficient descent nonlinear conjugate gradient method with inexact line search is proposed for solving the transformed unconstrained optimization problem. Under only one mild assumption, the global convergence of the proposed method is proved. Finally, to show the effectiveness of the proposed nonlinear conjugate gradient method, we compare it with three-term conjugate gradient method and Newton method. The numerical results show that the proposed nonlinear conjugate gradient method is potentially efficient.