On superlinear convergence of quasi-Newton methods for nonsmooth equations

Authors:
Liqun Qi
Affiliations:
-
Venue:
Operations Research Letters
Year:
1997

Citing 7
Cited 1

Newton's method for B-differentiable equations

Mathematics of Operations Research
On concepts of directional differentiability

Journal of Optimization Theory and Applications
Convergence analysis of some algorithms for solving nonsmooth equations

Mathematics of Operations Research
Local convergence of quasi-Newton methods for B-differentiable equations

Mathematical Programming: Series A and B
A family of variable metric proximal methods

Mathematical Programming: Series A and B
Convergence of the BFGS Method for LC1 Convex Constrained Optimization

SIAM Journal on Control and Optimization
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)

Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)

A primal-dual algorithm for minimizing a sum of Euclidean norms

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We show that strong differentiability at solutions is not necessary for superlinear convergence of quasi-Newton methods for solving nonsmooth equations. We improve the superlinear convergence result of Ip and Kyparisis for general quasi-Newton methods as well as the Broyden method. For a special example, the Newton method is divergent but the Broyden method is superlinearly convergent.