New Results on Superlinear Convergence of Classical Quasi-Newton Methods

Anton Rodomanov () and Yurii Nesterov ()
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Anton Rodomanov: Catholic University of Louvain
Yurii Nesterov: Catholic University of Louvain

Journal of Optimization Theory and Applications, 2021, vol. 188, issue 3, No 7, 744-769

Abstract: 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.

Keywords: Quasi-Newton methods; Convex Broyden class; DFP; BFGS; Superlinear convergence; Local convergence; Rate of convergence; 90C53; 90C30; 68Q25 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-020-01805-8

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