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Rates of superlinear convergence for classical quasi-Newton methods.
- Source :
-
Mathematical Programming . Jul2022, Vol. 194 Issue 1/2, p159-190. 32p. - Publication Year :
- 2022
-
Abstract
- We study the local convergence of classical quasi-Newton methods for nonlinear optimization. Although it was well established a long time ago that asymptotically these methods converge superlinearly, the corresponding rates of convergence still remain unknown. In this paper, we address this problem. We obtain first explicit non-asymptotic rates of superlinear convergence for the standard quasi-Newton methods, which are based on the updating formulas from the convex Broyden class. In particular, for the well-known DFP and BFGS methods, we obtain the rates of the form (n L 2 μ 2 k) k / 2 and (nL μ k) k / 2 respectively, where k is the iteration counter, n is the dimension of the problem, μ is the strong convexity parameter, and L is the Lipschitz constant of the gradient. [ABSTRACT FROM AUTHOR]
- Subjects :
- *QUASI-Newton methods
*TIME
*STANDARDS
Subjects
Details
- Language :
- English
- ISSN :
- 00255610
- Volume :
- 194
- Issue :
- 1/2
- Database :
- Academic Search Index
- Journal :
- Mathematical Programming
- Publication Type :
- Academic Journal
- Accession number :
- 157667594
- Full Text :
- https://doi.org/10.1007/s10107-021-01622-5