Some Studies On Memory Gradient Method For Unconstrained Optimization Problems

The method for solving unconstrained optimization is an important branch in optimization methods. Among many unconstrained optimization methods, the memory gradient method and super-memory gradient method generate the next iteration point by using the previous iterative information. Because of strong convergence and little calculation effort, these algorithms have a wide application.The main results in the dissertation are achieved as follows:In chapter 2, a modification to a memory gradient without line search is given, which expands the existing algorithm in the literature; In chapter 3, a new super-memory gradient method for unconstrained optimization problem is proposed. Since this algorithm only solve a system of linear equations instead of a quadratic subproblem with a trust region bound, the computational efficiency is improved; In chapter 4, a implementation version is given for the trust region gradient method with memory model. Numerical results show that this scheme is feasible.