大规模无约束优化的一族LBFGS类算法

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...

A class of limited memory BFGS-type algorithms for large-scale unconstrainedoptimization

In this paper, objective function value information is exploited in limited memory BFGS-type algorithms. we first construct a new quadratic function satisfying some interpolation conditions to approximate the objective function, get a new weak secant equation. Combining the new weak secant equation and that obtained by Yuan\cite{yuan1991}, a class of limited memory BFGS--type algorithms including the classic LBFGS algorithm based on a new weak secant equation are 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 quiet well.