Quasi-Newton methods in infinite-dimensional spaces and application to matrix equations

Abstract

Nonlinear equations, Optimization problems, Quasi-Newton methods, Rate of convergence, Linear convergence, Superlinear convergence, Hilbert space, Matrix equations, Algebraic Riccati equation,

Local convergence of quasi-Newton methods under metric regularity

“…There are quite a few papers dealing with quasi-Newton methods for solving the nonlinear equations in the infinite-dimensional setting, and some of them use the Broyden update, see e.g. [3], [13], [15], [18], [22], [23], [25]. In some of these papers, such as [15] and [18], Y is a Banach space; in [15] X is also a Banach space having a continuous inner product, and with (27) being defined on the completion of X in the norm induced by this inner product.…”