求解约束优化问题的记忆梯度Goldstein-Lavintin-Polyak投影算法

给求解无约束规划问题的记忆梯度算法中的参数一个特殊取法,得到目标函数的记忆梯度G o ldste in-L av in tin-Po lyak投影下降方向,从而对凸约束的非线性规划问题构造了一个记忆梯度G o ldste in-L av in tin-Po lyak投影算法,并在一维精确步长搜索和去掉迭代点列有界的条件下,分析了算法的全局收敛性,得到了一些较为深刻的收敛性结果.同时给出了结合FR,PR,HS共轭梯度算法的记忆梯度G o ldste in-L av in tin-Po lyak投影算法,从而将经典共轭梯度算法推广用于求解凸约束的非线性规划问题.数值例子表明新算法比梯度投影算法有效.

Memory Gradient Goldstein-Lavintin-Polyak Projection Method For Convex Constraints Problems

In this paper,a generalized memory gradient projection method for convex constrained optimization is presented by using Goldstein Lavintin Polyak projection.Conditions are given on the scalar to ensure that the general memory gradient projection direction is descent.The global convergence properties of the new method are discussed with an accurate step size rule and without assuming that the sequence of iteration is bounded.Combining FR,PR,HS methods with our new method,three new classes of memory gradient projection methods with conjugate gradient scalar are presented.The new methods use little storage,thus the methods are attractive for large scale problems.Numerical results show that the algorithm is efficient by comparing with Goldstein Lavintin Polyak gradient projection method.