Abstract
We present a new theoretical analysis of local superlinear convergence of classical quasi-Newton methods from the convex Broyden class. As a result, we obtain a significant improvement in the currently known estimates of the convergence rates for these methods. In particular, we show that the corresponding rate of the Broyden–Fletcher–Goldfarb–Shanno method depends only on the product of the dimensionality of the problem and the logarithm of its condition number.
Highlights
We study local superlinear convergence of classical quasi-Newton methods for smooth unconstrained optimization
The two most famous examples of quasi-Newton algorithms are the Davidon–Fletcher–Powell (DFP) [1,2] and the Broyden–Fletcher–Goldfarb–Shanno (BFGS) [3,4,5,6,7] methods, which together belong to the Broyden family [8] of quasi-Newton algorithms
We have presented a new theoretical analysis of local superlinear convergence of classical quasi-Newton methods from the convex Broyden class
Summary
We study local superlinear convergence of classical quasi-Newton methods for smooth unconstrained optimization. These algorithms can be seen as an approximation of the standard Newton method, in which the exact Hessian is replaced by some operator, which is updated in iterations by using the gradients of the objective function. The two most famous examples of quasi-Newton algorithms are the Davidon–Fletcher–Powell (DFP) [1,2] and the Broyden–Fletcher–Goldfarb–Shanno (BFGS) [3,4,5,6,7] methods, which together belong to the Broyden family [8] of quasi-Newton algorithms. For. Journal of Optimization Theory and Applications (2021) 188:744–769 an introduction into the topic, see [9] and [10, Chapter 6]. See [11] for the discussion of quasi-Newton algorithms in the context of nonsmooth optimization
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
