A limited memory BFGS-type method for large-scale unconstrained optimization

In this paper, a new numerical method for solving large-scale unconstrained optimization problems is presented. It is derived from a modified BFGS-type update formula by Wei, Li, and Qi. It is observed that the update formula can be extended to the framework of limited memory scheme with hardly more storage or arithmetic operations. Under some suitable conditions, the global convergence property is established. The implementations of the method on a set of CUTE problems indicate that this extension is beneficial to the performance of the algorithm.