On the relation between two local convergence theories of least-change secant update methods

Abstract

In this paper, we show that the main results of the local convergence theory for least-change secant update methods of Dennis and Walker (SIAM J. Numer. Anal. 18 (1981), 949-987) can be proved using the theory introduced recently by Martinez (Math. Comp. 55 (1990), 143-167). In addition, we exhibit two generalizations of well-known methods whose local convergence can be easily proved using Martinez's theory.

Convergence of the BFGS Method for $LC^1 $ Convex Constrained Optimization

“…See [3], [4], [11], [12], [14], [22]. The local convergence theory of quasi-Newton methods for smooth equations and smooth unconstrained minimization problems is well developed.…”