一类新的曲线搜索下的记忆梯度法

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.算法采用曲线搜索方法,在每一步同时确定搜索方向和步长,收敛稳定,并且不需计算和存储矩阵,适于求解大规模优化问题.数值试验表明算法是有效的.

A New Class of Memory Gradient Method with Curve Search Rule

This paper presents a new class of memory gradient method for unconstrained optimization problems. The global convergence and linear convergence rate are proved under some mild conditions. This method uses some curve search rules to determine the search direction and the step-size simultaneously at each iteration, and avoids the computation and storage of some matrices associated with the Hessian of objective functions. This makes the method converge stably and be more suitable to solve large scale optimization problems. Numerical experiments show that our algorithm is available and effective in practical computation.