一个求解无约束优化的ODE型混合方法  

A Hybrid ODE-based Method for Unconstrained Optimization

作　　者：贾胜南 欧宜贵[1] 王冠舒 

机构地区：[1]海南大学数学系,海南海口570228 [2]胜利学院数学物理系,山东东营257097

出　　处：《应用数学》2015年第4期801-810,共10页Mathematica Applicata

基　　金：国家自然科学基金(11261015);海南省自然科学基金(111001;20151002)

摘　　要：基于非单调技术,本文给出一种新的求解无约束优化的ODE型算法.该算法的特点是:每次迭代时只解一次线性方程组系统而获得试验步,然后采用改进的非单调线搜索获得下一个迭代点,从而避免了重复求解线性方程组,减少了算法的计算量.在合理的假设条件下,该算法被证明是全局收敛和局部超线性收敛的.数值试验证实了该算法的有效性.This paper presents a new ODE-based method for unconstrained optimization. A feature of this proposed method is that at each iteration, a system of linear equation system is solved only once to obtain a direction. Then a modified nonmonotone line search along this direction is performed to generate a next point, thus avoiding resolving the linear equation and reducing the amount of calculation. Under some conditions, the global convergence and locally superlinear convergence rate are analyzed. Preliminary numerical results indicate that this algorithm is effective.

关 键 词：无约束优化 非单调技术 信赖域技术 收敛性分析 数值试验 

分 类 号：O221[理学—运筹学与控制论]