一类新的记忆梯度法及其收敛性

A New Memory Gradient Method and its Convergence

本文着重研究求解无约束优化问题的记忆梯度法,利用当前和前面一步迭代点的信息产生下降方向,采用Armijo线性搜索确定步长,得到了一类新的无约束优化算法。新算法在较弱的条件下具有全局收敛性和线性收敛速率,并且不用计算和存储矩阵,适于求解大规模优化问题。数值试验表明算法是有效的。

The memory gradient methods for unconstrained optimization problems were investigated. A new algorithm is presented which uses the current and previous one-step iterative information to generate a decent direction, and uses an Armijo linear search to determine the step-size. The new method converges globally and it has a linear convergence rate under some mild conditions. Moreover, the method avoids the computation and storage of some matrices. It is suitable for solving large scale optimization problems. Experimental results show that the new method is effcient in practical com- putation.