A closed-form bound on the asymptotic linear convergence of iterative methods via fixed point analysis

نویسندگان

چکیده

In many iterative optimization methods, fixed-point theory enables the analysis of convergence rate via contraction factor associated with linear approximation operator. While this characterizes asymptotic convergence, it does not explain non-linear behavior these algorithms in non-asymptotic regime. letter, we take into account effect first-order error and present a closed-form bound on terms number iterations required for distance between iterate limit point to reach an arbitrarily small fraction initial distance. Our includes two terms: one corresponds linearized version operator other overhead error. With focus scalar case, tightness proposed is proven positively quadratic difference equations.

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ژورنال

عنوان ژورنال: Optimization Letters

سال: 2022

ISSN: ['1862-4480', '1862-4472']

DOI: https://doi.org/10.1007/s11590-022-01893-7