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This paper proposes an accelerated proximal point method for maximally monotone operators.
Arxiv 1905.06030
Gu, G., Yang, J.: On the optimal ergodic sublinear convergence rate of the relaxed proximal point algorithm for variational inequalities (2019) · 1905
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SIAM J. Numer. Anal. 16
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Nesterov, Y.: A method for unconstrained convex minimization problem with the rate of convergence O ( 1 / k 2 ) O(1/k^{2}) · 1983
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Güler, O.: On the convergence of the proximal point algorithm for convex minimization · 1991
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Eckstein, J., Bertsekas, D.P.: On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators · 1992
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Güler, O.: New proximal point algorithms for convex minimization · 1992
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Set-Valued Analysis 9
Alvarez, F., Attouch, H.: An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping · 2001
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SIAM J. Imaging Sci. 2
Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems · 2009
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SIAM J. Imaging Sci. 3
Esser, E., Zhang, X., Chan, T.: A general framework for a class of first order primal-dual algorithms for convex optimization in imaging science · 2010
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Bauschke, H.H., Combettes, P.L.: Convex analysis and monotone operator theory in Hilbert spaces · 2011
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Su, W., Boyd, S., Candes, E.J.: A differential equation for modeling Nesterov’s accelerated gradient method: theory and insights · 2016
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SIAM J. Optim. 27
Taylor, A.B., Hendrickx, J.M., Glineur, F.: Exact worst-case performance of first-order methods for composite convex optimization · 2017
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Mathematical Programming 161
Taylor, A.B., Hendrickx, J.M., Glineur, F.: Smooth strongly convex interpolation and exact worst-case performance of first-order methods · 2017
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Mathematical Programming 170
Combettes, P.L.: Monotone operator theory in convex optimization · 2018
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SIAM J. Optim. 28
Kim, D., Fessler, J.A.: Another look at the Fast Iterative Shrinkage/Thresholding Algorithm (FISTA) · 2018
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SIAM J. Optim. 28
Kim, D., Fessler, J.A.: Generalizing the optimized gradient method for smooth convex minimization · 2018
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Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging · 2011
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http://cvxr.com/cvx (2012)
CVX Research Inc.: CVX: Matlab software for disciplined convex programming, version 2.0 · 2012
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SIAM J. Imaging Sci. 5
He, B., Yuan, X.: Convergence analysis of primal-dual algorithms for a saddle-point problem: from contraction perspective · 2012
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Mathematical Programming 140
Nesterov, Y.: Gradient methods for minimizing composite functions · 2013
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SIAM J. Optim. 24
Corman, E., Yuan, X.: A generalized proximal point algorithm and its convergence rate · 2014
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Mathematical Programming 145
Drori, Y., Teboulle, M.: Performance of first-order methods for smooth convex minimization: A novel approach · 2014
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SIAM J. Imaging Sci. 7
Goldstein, T., O’Donoghue, B., Setzer, S., Baraniuk, R.: Fast alternating direction optimization methods · 2014
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Ph.D. thesis, Universitäts-und Landesbibliothek der Heinrich-Heine-Universität Düsseldorf (2018)
Lieder, F.: Projection based methods for conic linear programming-optimal first order complexities and norm constrained quasi newton methods · 2018
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J. Mach. Learning Res. 18
Lin, H., Mairal, J., Harchaoui, Z.: Catalyst acceleration for first-order convex optimization: from theory to practice · 2018
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Arxiv 1810.08907
Shi, B., Du, S.S., Jordan, M.I., Su, W.J.: Understanding the acceleration phenomenon via high-resolution differential equations (2018) · 2018
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Appl. Math. Optim. 80
Attouch, H., Cabot, A.: Convergence of a relaxed inertial forward-backward algorithm for structured monotone inclusions · 2019
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SIAM J. Optim. 29
Attouch, H., Chbani, Z., Riahi, H.: Fast proximal methods via time scaling of damped inertial dynamics · 2019
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Mathematical Programming 174
Attouch, H., Peypouquet, J.: Convergence of inertial dynamics and proximal algorithms governed by maximally monotone operators · 2019
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URL http://www2.isye.gatech.edu/~nemirovs/Lect_EMCO.pdf
Nemirovski, A.: Efficient methods in convex programming (1994) · 2019
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In: Proceedings of the Conference on Learning Theory, pp. 2934–2992 (2019)
Taylor, A.B., Bach, F.: Stochastic first-order methods: non-asymptotic and computer-aided analyses via potential functions · 2019
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Mathematical Programming 184
Attouch, H., Cabot, A.: Convergence of a relaxed inertial proximal algorithm for maximally monotone operators · 2020
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Mathematical Programming (2020)
Attouch, H., Chbani, Z., Fadili, J., Riahi, H.: First-order optimization algorithms via inertial systems with Hessian driven damping · 2020
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Mathematical Programming 184
Drori, Y., Taylor, A.B.: Efficient first-order methods for convex minimization: a constructive approach · 2020
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SIAM J. Optim. 30
Gu, G., Yang, J.: Tight sublinear convergence rate of the proximal point algorithm for maximal monotone inclusion problems · 2020
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J. Optim. Theory Appl. (2020)
Kim, D., Fessler, J.A.: Optimizing the efficiency of first-order methods for decreasing the gradient of smooth convex functions · 2020
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Optimization Letters 15
Lieder, F.: On the convergence rate of the Halpern-iteration · 2020
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SIAM J. Optim. 30
Ryu, E.K., Taylor, A.B., Bergeling, C., Giselsson, P.: Operator splitting performance estimation: tight contraction factors and optimal parameter selection · 2020
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URL https://large-scale-book.mathopt.com/LSCOMO.pdf
Ryu, E.K., Yin, W.: Large-scale convex optimization via monotone operators (2020) · 2021
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