一个基于非单调技术的超记忆梯度法

A Supermemory Gradient Method Based on the Nonmonotone Technique

本文给出一个修正的非单调线搜索策略,并结合该策略提出一个求解无约束优化问题的超记忆梯度算法.该算法的主要特点是:在每一次迭代中,它所产生的搜索方向总是满足充分下降条件.这一特性不依赖于目标函数的凸性以及方法所采用的线搜索策略.在较弱的条件下,该方法具有全局收敛和局部R-线性收敛性.数值实验表明了该方法的有效性.

In this paper,we present a modified nonmonotone strategy.Based on this strategy,a supermemory gradient method for unconstrained problems is proposed.An attractive property of the proposed method is that the search direction always provides sufficient descent step at each iteration.The property is independent of convexity of objective function and the line search used.Under mild assumptions,the global convergence and R-linear convergence properties of the proposed algorithm are established respectively.Numerical results are also reported to show that the proposed method is effective.