基于稀疏对角拟牛顿方向的非单调超记忆梯度算法

A Non-monotone Super-memory Gradient Method Based on the Diagonal-sparse Quasi-Newton Direction

超记忆梯度算法由于其迭代简单和较小的存储需求,在求解大规模无约束优化问题中起着特殊的作用.本文基于稀疏对角拟牛顿技术,结合修正Gu和Mo非单调线搜索步长规则,建立了求解大规模无约束最优化问题的非单调超记忆梯度新算法,给出了算法的全局收敛性分析.新算法具有算法稳定、计算简单的特点可用于求解病态和大规模问题.数值例子表明算法有效稳定.

The super-memory gradient method has played a special role for solving large-scale unconstrained optimization problems due to its simplicity and the very low storage. In this paper, by combining the diagonal-sparse quasi-Newton technique with the modified Gu and Mo non-monotone line search method, a new super-memory gradient method for unconstrained optimization problems is presented. The global convergence property of the new method is analyzed. The new method has two properties： it converges stably and can solve ill-conditioned problems, it only needs simple computation so as to solve large-scale problems. The numerical results show that the new method is effective and stable in practical computation.