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This paper investigates the optimal ergodic sublinear convergence rate of the relaxed proximal point algorithm for solving monotone variational inequality problems.
Proximité et dualité dans un espace hilbertien
J.-J. Moreau · 1965
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Régularisation d’inéquations variationnelles par approximations successives
B. Martinet · 1970
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Monotone operators and the proximal point algorithm
R. T. Rockafellar · 1976
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On the convergence of the proximal point algorithm for convex minimization
O. Güler · 1991
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New proximal point algorithms for convex minimization
O. Güler · 1992
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Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones
J. F. Sturm · 1999
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The proximal point algorithm with genuine superlinear convergence for the monotone complementarity problem
N. Yamashita and M. Fukushima · 2000
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Finite-dimensional variational inequalities and complementarity problems. Vol. I
F. Facchinei and J.-S. Pang · 2003
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Quadratic matrix programming
A. Beck · 2006
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Primal-dual subgradient methods for convex problems
Y. Nesterov · 2009
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On the O ( 1 / n ) O(1/n) convergence rate of the Douglas-Rachford alternating direction method
B. He and X. Yuan · 2012
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Performance of first-order methods for smooth convex minimization: a novel approach
Y. Drori and M. Teboulle · 2014
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Customized proximal point algorithms for linearly constrained convex minimization and saddle-point problems: a unified approach
G. Gu, B. He, and X. Yuan · 2014
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An optimal variant of Kelley’s cutting-plane method
Y. Drori and M. Teboulle · 2016
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Optimized first-order methods for smooth convex minimization
D. Kim and J. A. Fessler · 2016
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Convex analysis and monotone operator theory in Hilbert spaces
H. H. Bauschke and P. L. Combettes · 2017
Exact worst-case performance of first-order methods for composite convex optimization
A. B. Taylor, J. M. Hendrickx, and F. Glineur · 2017
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Smooth strongly convex interpolation and exact worst-case performance of first-order methods
A. B. Taylor, J. M. Hendrickx, and F. Glineur · 2017
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Another look at the fast iterative shrinkage/thresholding algorithm (FISTA)
D. Kim and J. A. Fessler · 2018
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Generalizing the optimized gradient method for smooth convex minimization
D. Kim and J. A. Fessler · 2018
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D. Kim and J. A. Fessler · 2018
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On the worst-case complexity of the gradient method with exact line search for smooth strongly convex functions
E. de Klerk, F. Glineur, and A. B. Taylor · 2017
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On the convergence analysis of the optimized gradient method
D. Kim and J. A. Fessler · 2017
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Convex interpolation and performance estimation of first-order methods for convex optimization
A. B. Taylor · 2017
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E. K. Ryu, A. B. Taylor, C. Bergeling, and P. Giselsson · 2018
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Exact worst-case convergence rates of the proximal gradient method for composite convex minimization
A. B. Taylor, J. M. Hendrickx, and F. Glineur · 2018
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G. Gu and J. Yang · 2019
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Accelerated proximal point method for maximally monotone operators
D. Kim · 2019
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