Diagonal quasi-Newton methods via least change updating principle with weighted Frobenius norm

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of least change updating technique analogous to that for the DFP method except that the full quasi-Newton matrix has been replaced by some diagonal matrix.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.