A class of superlinearly convergent projection quasi-Newton algorithms

In this paper, the authors give a class of algorithms containing two parameters for nonlinear programming problems with linear constraints by combining the gradient projection with quasi-Newton method. Its global convergence and superlinear rate of convergence are proved under suitable conditions, and some special examples of this algorithm are given, such as the Davidon–Fletcher–Powell projection method, the Broyden–Fletcher–Goldfarb–Shanno projection method and so on.