Research On Gradient Algorithm Of M-tensor Equation

With the widespread use of tensors in image processing,engineering technology and other fields,tensors and its related optimization problems have been widely concerned and studied.As a kind of important tensor optimization problem,tensor equation problems are widely used in engineering,data mining,signal processing and other related fields.This thesis mainly studies the solving algorithm of M-tensor equation problems.The details are as follows:In the first chapter,we introduce the background of M-tensors and M-tensor equation problems,give relevant definitions and properties of M-tensors and M-tensor equation problems,and the properties of the solution for M-tensor equation problems.In the second chapter,we give the steepest descent method for solving M-tensor equation problems.The global convergence property of the algorithm is given under the Armijo line search,and numerical experiments show that the algorithm can effectively solve M-tensor equation problems.In the third chapter,we give a three-term conjugate gradient method for solving M-tensor equation problems.The algorithm is based on the Armijo line search,under the certain assumption,we obtain the global convergence property of the algorithm.Numerical experiments show that the algorithm can effectively solve M-tensor equation problems.In the fourth chapter,we give a conjugate gradient method with the Wolfe-type line search for solving M-tensor equation problems.The algorithm has the sufficient descent property,based on the properties of M-tensors,under the certain assumption,we obtain the global convergence property of the algorithm.Numerical experiments also show that the algorithm can effectively solve M-tensor equation problems.