A Class of Revised Broyden Algorithms Without Exact Line Search (Journal of Computational Mathematics, 2004)
In this paper, we discuss the convergence of the Broyden algorithms with revised search direction. Under some inexact line searches, we prove that the algorithms are globally convergent for continuously differentiable functions and the rate of local convergence of the algorithms is one-step superlinear and n-step second-order for uniformly convex objective functions.
Keywords: Variable metric algorithms; Line search; Convergence; Convergence rate.