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This paper investigates optimal error bounds and convergence rates for general Mann iterations for computing fixed-points of non-expansive maps.
Mean value methods in iteration
Mann W.R., · 1953
Earlier work this paper cites.
Two remarks on the method of successive approximations
Krasnosel’skiĭ M.A., · 1955
Earlier work this paper cites.
Extension of uniformly continuous transformations and hyperconvex metric spaces
Aronszajn N. and Panitchpakdi P., · 1956
Earlier work this paper cites.
On the distribution of the number of successes in independent trials
Hoeffding W., · 1956
Earlier work this paper cites.
On the distribution of the number of successes in independent trials
Darroch J.N., · 1964
Earlier work this paper cites.
The solution by iteration of nonlinear functional equations in Banach spaces
Browder F.E. and Petryshyn W.V., · 1966
Earlier work this paper cites.
Convergence of approximants to fixed points of non-expansive nonlinear mappings in Banach spaces
Browder F.E., · 1967
Earlier work this paper cites.
Fixed points of nonexpanding maps
Halpern B., · 1967
Earlier work this paper cites.
Fixed point iterations of non-expansive mappings
Reich S., · 1975
Earlier work this paper cites.
On the asymptotic behavior of non-expansive mappings and semigroups in Banach spaces
Baillon J.B., Bruck R.E. and Reich S., · 1978
Earlier work this paper cites.
Weak convergence theorems for non-expansive mappings in Banach spaces
Reich S., · 1979
Earlier work this paper cites.
Strong convergence theorems for resolvents of accretive operators in Banach spaces
Reich S., · 1980
Earlier work this paper cites.
Computationally efficient bounds for the Catalan numbers
Dutton R.D. and Brigham R.C., · 1986
Earlier work this paper cites.
Optimal rates of asymptotic regularity for averaged non-expansive mappings
Baillon J.B. and Bruck R.E., · 1992
Cited alongside, same era.
Krasnoselski-Mann iterations in normed spaces
Borwein J., Reich S. and Shafrir I., · 1992
Cited alongside, same era.
Approximation of fixed points of non-expansive mappings
Wittmann R., · 1992
Cited alongside, same era.
Approximating fixed points of nonexpansive mappings
Reich S., · 1994
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The rate of asymptotic regularity is o ( 1 / n ) o(1/\sqrt{n})
Baillon J.B. and Bruck R.E., · 1996
Cited alongside, same era.
Iterative algorithms for nonlinear operators
Xu H-K., · 2002
Cited alongside, same era.
On the rate of convergence of Krasnosel’skiĭ-Mann iterations and their connection with sums of Bernoullis
Cominetti R., Soto J.A. and Vaisman J., · 2014
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Performance of first-order methods for smooth convex minimization: a novel approach
Drori Y. and Teboulle M., · 2014
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Quantitative results for Halpern iterations of non-expansive mappings
Körnlein D., · 2015
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A first order method for solving convex bilevel optimization problems
Sabach S. and Shtern S., · 2017
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Sharp convergence rates for averaged non-expansive maps
Bravo M. and Cominetti R., · 2018
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Lectures on Convex Optimization , Springer Optimization and Its Applications , vol. 137
Nesterov Y., · 2018
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