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We derive an equivalent form of Halpern's fixed-point iteration scheme for solving a co-coercive equation (also called a root-finding problem), which can be viewed as a Nesterov's accelerated interpretation.
Some methods of speeding up the convergence of iteration methods
Boris T. Polyak · 1964
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Fixed points of nonexpanding maps
B. Halpern · 1967
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An extragradient method for finding saddle-points and for other problems
G. M. Korpelevic · 1976
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Monotone operators and the proximal point algorithm
R.T. Rockafellar · 1976
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Splitting algorithms for the sum of two nonlinear operators
P. L. Lions and B. Mercier · 1979
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A modification of the Arrow-Hurwicz method for search of saddle points
L. D. Popov · 1980
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A method for unconstrained convex minimization problem with the rate of convergence 𝒪 ( 1 / k 2 ) \mathcal{O}(1/k^{2})
Y. Nesterov · 1983
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Approximation of fixed points of nonexpansive mappings
R. Wittmann · 1992
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The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space
H. Bauschke · 1996
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A modified forward-backward splitting method for maximal monotone mappings
P. Tseng · 2000
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Iterative algorithms for nonlinear operators
H.-K. Xu · 2002
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Finite-dimensional variational inequalities and complementarity problems
F. Facchinei and J.-S. Pang · 2003
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Prox-method with rate of convergence 𝒪 ( 1 / t ) \mathcal{O}(1/t) for variational inequalities with Lipschitz continuous monotone operators and smooth convex-concave saddle point problems
A. Nemirovskii · 2004
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Introductory lectures on convex optimization: A basic course
Y. Nesterov · 2004
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Variational Analysis
R. Rockafellar and R. Wets · 2004
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Signal recovery by proximal forward-backward splitting
P. L. Combettes and V. R. Wajs · 2005
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Smooth minimization of non-smooth functions
Y. Nesterov · 2005
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Set-Valued Mappings and Enlargements of Monotone Operators
R. S. Burachik and A. Iusem · 2008
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A fast iterative shrinkage-thresholding algorithm for linear inverse problems
A. Beck and M. Teboulle · 2009
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Convex functions, monotone operators and differentiability
R. R. Phelps · 2009
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On the complexity of the hybrid proximal extragradient method for the interates and the ergodic mean
R.D.C. Monteiro and B.F. Svaiter · 2010
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A differential equation for modeling Nesterov’s accelerated gradient method: Theory and insights
W. Su, S. Boyd, and E. Candes · 2014
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A geometric alternative to Nesterov’s accelerated gradient descent
S. Bubeck, Y. T. Lee, and M. Singh · 2015
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On the convergence of the iterates of the “Fast iterative shrinkage/thresholding algorithm”
A. Chambolle and C. Dossal · 2015
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Efficient methods for structured nonconvex-nonconcave min-max optimization
J. Diakonikolas, C. Daskalakis, and M. Jordan · 2021
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A. d’Aspremont, D. Scieur, and A. Taylor · 2021
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Accelerated proximal point method for maximally monotone operators
D. Kim · 2021
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Fast extra gradient methods for smooth structured nonconvex-nonconcave minimax problems
S. Lee and D. Kim · 2021
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On the convergence rate of the halpern-iteration
F. Lieder · 2021
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Accelerated proximal algorithms with a correction term for monotone inclusions
P.-E. Maingé · 2021
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B. He and X. Yuan · 2015
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Quantitative results for Halpern iterations of nonexpansive mappings
D. Körnlein · 2015
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Projected reflected gradient methods for monotone variational inequalities
Y. Malitsky · 2015
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The rate of convergence of Nesterov’s accelerated forward-backward method is actually faster than 𝒪 ( 1 / k 2 ) \mathcal{O}(1/k^{2})
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