一个新的求解无约束优化问题的超记忆梯度法

基金项目:

河南省教育厅科学技术研究重点项目(13A110767)

详细信息

A New Super-memory Gradient Method for Solving Unconstrained Optimization Problems

College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, China

摘要: 提出一个新的求解无约束优化问题的超记忆梯度法.该算法在每步迭代中充分利用前面迭代点的信息产生下降方向,利用曲线搜索产生步长,并且在每步迭代中不需计算和存储矩阵,适于求解大规模优化问题.在较弱的条件下证明了算法具有全局收敛性和线性收敛速度.数值实验表明该算法是有效的
- 无约束优化 /
- 曲线搜索 /
- 全局收敛 /
- 线性收敛速度
Abstract: A new super-memory gradient method for solving unconstrained optimization problems was proposed. A new search direction was generated by using the current and previous multi-step iterative information in the proposed method, and the step-size at each iteration was defined by a curve search rule, which can be used to solve large scale unconstrained optimization problems because it avoids the computation and storage of some matrices. Furthermore, the global convergence and the convergence rate of the new algorithm were proved under some weak conditions. Finally, numerical results showed that the proposed algorithm is effective
- unconstrained optimization /
- curve search /
- global convergence /
- linear convergence rate

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[2]	汤京永，秦金华，董丽．无约束优化的超记忆梯度法及其全局收敛性［J］．信阳师范学院学报: 自然科学版，2008， 21( 1) : 12-14．