摘要
尝试在有限存储类算法中利用目标函数值所提供的信息.首先利用插值条件构造了一个新的二次函数逼近目标函数,得到了一个新的弱割线方程,然后将此弱割线方程与袁[1]的弱割线方程相结合,给出了一族包括标准LBFGS的有限存储BFGS类算法,证明了这族算法的收敛性.从标准试验函数库CUTE中选择试验函数进行了数值试验,试验结果表明这族算法的数值表现都与标准LBFGS类似.
In this paper, value information of objective function is exploited in limited memory BFGS-type algorithms. We first construct a new quadratic function satisfying some interpolation conditions to approximate the objective function, and get a new weak secant equation. Combining the new weak secant equation with that obtained by Yuan[1], a class of limited memory BFGS-type algorithms including the classic LBFGS algorithm based on a new weak secant equation is proposed. The convergence of this class limited memory BFGS-type algorithms is proved. Numerical results for standard test problems from CUTE are reported, which indicate that all the algorithms in the proposed class perform quite well.
出处
《运筹学学报》
CSCD
2011年第3期9-18,共10页
Operations Research Transactions
基金
the National Natural Science Foundation of China(71071075)
the Natural Science Project of Nanjing University of Technology(39704017)
关键词
无约束优化
弱割线方程
BFGS算法
收敛性分析
有限存储
unconstrained optimization, weak secant equation, BFGS algorithm convergence analysis, limited memory
