一类新的曲线搜索下的多步下降算法  

A New Class of Multi-step Descent Methods with Curve Search Rule

作　　者：汤京永[1,2] 董丽[2] 李学志[2] 

机构地区：[1]上海交通大学数学系,上海200240 [2]信阳师范学院数学与信息科学学院,河南信阳464000

出　　处：《应用数学》2009年第4期815-820,共6页Mathematica Applicata

基　　金：国家自然科学基金项目(10671166)

摘　　要：提出一类新的曲线搜索下的多步下降算法,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.算法利用前面多步迭代点的信息和曲线搜索技巧产生新的迭代点,收敛稳定,不用计算和存储矩阵,适于求解大规模优化问题.数值试验表明算法是有效的.This paper presents a new class of multi-step descent methods with curve search rule. We prove its global convergence and linear convergence rate under some mild conditions. The methods use to generate new iterative poin and be more suitable to solve and storage of some matrices. pr ts evious multi-step iterative information and curve search rule at each iteration. This makes the new method converge stably large scale optimization problems by avoiding the computation Numerical experiments show that the new method is available and efficient in practical computation.

关 键 词：无约束优化 曲线搜索 全局收敛性 线性收敛速率 

分 类 号：O221.2[理学—运筹学与控制论]