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中文摘要：
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．
英文摘要：
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.
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