On the Characterization of q-Superlinear Convergence of Quasi-Newton Methods for Constrained Optimization

: In this note, the authors present what they consider to be a short, direct, and self-contained derivation of the Boggs-Tolle-Wang characterization of q-superlinear convergence for quasi-Newton methods for constrained optimization. While they have stated that the three previous derivations (Boggs, Tolle, and Wang; Fontecilla, Steihaug, and Tapia; and Nocedal and Overton) leave something to be desired, they quickly add that the present work was strongly influenced by these three papers. Indeed, the basic idea that led to the present derivation was to attempt to parallel the Nocedal-Overton derivation using a formulation of the quasi-Newton method that possessed the attribute that all necessary differentiations could be obtained in a straightforward manner. As they have seen, one of the formulations suggested by Tapia possesses this property.