一类新的Wolfe线性搜索下的记忆梯度法

A new class of memory gradient methods with Wolfe line search

提出一类新的求解无约束优化问题的记忆梯度法,在较弱条件下证明了算法具有全局收敛性和线性收敛速率。算法在每步迭代中利用当前和前面迭代点的信息产生下降方向,不需计算和存储矩阵,适于求解大规模优化问题。初步的数值试验表明算法比Wolfe搜索下的FR,PRP和HS共轭梯度法及最速下降法有效。

A new class of memory gradient methods for unconstraind optimization problems was presented. Its global convergence and linear convergence rate were proved under some mild conditions. The methods are suitable to solve large scale optimization problems by using the current and previous iterative information, which generate the descent direction and avoiding the computation and the storage of some matrices. Numerical experiments show that the new methods are more efficient then FR, PRP, HS conjugate gradient methods and the steepest descent method under the condition of the Wolfe line search.