一个新的超记忆梯度法及全局收敛性  

A New Supermemory Gradient Method and the Global Convergence

作　　者：李双安[1] 陈凤华[1] 程慧燕[1] 

机构地区：[1]河南理工大学万方科技学院公共基础教学部,河南郑州450026

出　　处：《海南师范大学学报（自然科学版）》2015年第3期237-241,共5页Journal of Hainan Normal University（Natural Science）

基　　金：国家自然科学基金(11361018);广西杰出青年基金(2012GXSFFA060003);河南省教育厅科学技术研究重点项目(12B110011);高等学校重点科研项目(15B110008)

摘　　要：文章提出了一个新的超记忆梯度法解决无约束优化问题.该算法沿着目标函数的下降方向进行搜索,每步迭代提出的算法都充分地利用了前面多步迭代信息,避免目标函数海瑟阵的储存和计算,因此它适合解决大规模无约束优化问题.在适当的假设条件下,证明了所提出的算法具有全局收敛性.数值实验表明此算法的可行性.In this paper, we propose a new supermemory gradient method for unconstrained optimization. An attractive property of the proposed method is that the direction generated by the method is always a descent for the objective function. The proposed method sufficiently uses the previous multi-step iterative information at each iteration and avoids the storage and computation of matrices associated with the Hessian of objective functions. Therefore, it is suitable to solve large-scale unconstrained optimization problems. Under appropriate conditions, we show that the new supermemory gradient method with nonmonotone line search is globally convergent. Numerical experiments show that the proposed algorithm is effective.

关 键 词：无约束优化 超记忆梯度法 非单调线搜索 全局收敛性 数值实验 

分 类 号：O224[理学—运筹学与控制论]