A Class Of Modified Gradient Projection Algorithms For Convex Constrained Problems

In this paper, we propose two new methods of the Goldstein-Levitin-Polyak(GLP) projected gradient algorithm for nonlinear convex constrained optimization. The main contents of the thesis are presented as follows:(1) Based on the modified quasi-Newton equation, and combining Goldstein -Levitin-Polyak(GLP) projection technique, this article establishes a non-monotone variable dimension gradient projection algorithm with convex sets constraints for optimization problem. The new algorithm proves the convergence and the attainment of unit step length and the Q super linear convergence rate in certain conditions. The determination of step length is divided into two stages. The first stage choices an unconstrained step and then uses projection to determination the feasible drop direction of algorithm. The second stage uses non-monotone line search technology to determine the next iteration. Numerical experiments show that our algorithm is effective and is suitable for solving large-scale problems.(2) Based on the modified quasi-Newton equation, and combining Goldstein -Levitin-Polyak(GLP) projection technique with Zhang H.C non-monotone technique, this article establishes a Zhang H.C non-monotone variable dimension gradient projection algorithm with convex sets constraints for optimization problem. The new algorithm proves the convergence and the attainment of unit step length and the Q super linear convergence rate in certain conditions. The determination of step length is divided into two stages. The first stage choices an unconstrained step and then uses projection to determination the feasible drop direction of algorithm. The second stage uses Zhang H.C non-monotone line search technology to determine the next iteration. Numerical experiments show that our algorithm is effective and is suitable for solving large-scale problems.