A Class of Modified Broyden Algorithms

Abstract

In this paper we discuss the convergence of the modified Broyden algorithms. We prove that the algorithms are globally convergent for the continuous differentiable function and the rate of convergence of the algorithms is one-step superlinear and n-step second-order for the uniformly convex objective function. From the discussion of this paper, we may get some convergence properties of the Broyden algorithms.