This paper presents a class of low memory quasi-Newton methods with standard backtracking line search for large-scale unconstrained minimization. The methods are derived by means of least change updating technique analogous to that for the DFP method except that the full quasi-Newton matrix has been replaced by some diagonal matrix. We establish convergence properties for some particular members of the class under line search with Armijo condition. Sufficient conditions for the methods to be superlinearly convergent are also given. Numerical results are then presented to illustrate the usefulness of these methods in large-scale minimization.

中文翻译：

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基于加权Frobenius范数的最小变化更新原理的对角拟牛顿法

本文提出了一种带有标准回溯线搜索的低内存准牛顿方法，用于大规模无约束最小化。这些方法是通过类似于DFP方法的最小变化更新技术来推导的，不同之处在于，已用对角线矩阵代替了完整的拟牛顿矩阵。我们在Armijo条件下通过线搜索为类的某些特定成员建立收敛属性。还给出了方法达到超线性收敛的充分条件。然后给出数值结果，以说明这些方法在大规模最小化中的有用性。