A class of rank-one positive definite qnasi-newton updates for unconstrained minimization2

We introduce variationally a class of rank-one Quasi-Newton updates, which is a subset of the generalized Huang-Oren class. We show that this class contains two disjoint subclasses of positive definite updates. One optimally conditioned update in the sense of Oren and Spedicato is shown to exist in each of the two subclasses. Some criteria for selection of the remaining degrees of freedom and some numerical experiments are discussed.