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Proximal operations are among the most common primitives appearing in both practical and theoretical (or high-level) optimization methods.
Transactions of the American Mathematical Society 82
Douglas, J., Rachford, H.H.: On the numerical solution of heat conduction problems in two and three space variables · 1956
Earlier work this paper cites.
Comptes rendus hebdomadaires des séances de l’Académie des sciences de Paris 255
Moreau, J.J.: Fonctions convexes duales et points proximaux dans un espace hilbertien · 1962
Earlier work this paper cites.
USSR Computational Mathematics and Mathematical Physics 4
Polyak, B.T.: Some methods of speeding up the convergence of iteration methods · 1964
Earlier work this paper cites.
Proceedings of the American Mathematical Society 16
Brøndsted, A., Rockafellar, R.T.: On the subdifferentiability of convex functions · 1965
Earlier work this paper cites.
Bulletin de la Société mathématique de France 93
Moreau, J.J.: Proximité et dualité dans un espace hilbertien · 1965
Earlier work this paper cites.
Revue Française d’Informatique et de Recherche Opérationnelle 4
Martinet, B.: Régularisation d’inéquations variationnelles par approximations successives · 1970
Earlier work this paper cites.
Comptes rendus hebdomadaires des séances de l’Académie des sciences de Paris 274
Martinet, B.: Détermination approchée d’un point fixe d’une application pseudo-contractante. cas de l’application prox · 1972
Earlier work this paper cites.
Mathematical programming 5
Rockafellar, R.T.: A dual approach to solving nonlinear programming problems by unconstrained optimization · 1973
Earlier work this paper cites.
Bulletin of the American Mathematical Society 81
Bruck Jr, R.E.: An iterative solution of a variational inequality for certain monotone operators in Hilbert space · 1975
Earlier work this paper cites.
Mathematics of operations research 1
Rockafellar, R.T.: Augmented Lagrangians and applications of the proximal point algorithm in convex programming · 1976
Earlier work this paper cites.
SIAM journal on control and optimization 14
Rockafellar, R.T.: Monotone operators and the proximal point algorithm · 1976
Earlier work this paper cites.
SIAM Journal on Numerical Analysis 16
Lions, P.L., Mercier, B.: Splitting algorithms for the sum of two nonlinear operators · 1979
Earlier work this paper cites.
Journal of Mathematical Analysis and Applications 72
Passty, G.B.: Ergodic convergence to a zero of the sum of monotone operators in Hilbert space · 1979
Earlier work this paper cites.
In: M. Fortin, R. Glowinski (eds.) Augmented Lagrangian Methods: Applications to the Solution of Boundary-Value Problems. North-Holland:Amsterdam (1983)
Fortin, M., Glowinski, R.: On decomposition-coordination methods using an Augmented Lagrangian · 1983
Earlier work this paper cites.
In: M. Fortin, R. Glowinski (eds.) Augmented Lagrangian Methods: Applications to the Solution of Boundary-Value Problems. North-Holland:Amsterdam (1983)
Gabay, D.: Applications of the method of multipliers to variational inequalities · 1983
Earlier work this paper cites.
Soviet Mathematics Doklady 27
Nesterov, Y.: A method of solving a convex programming problem with convergence rate O( 1 / k 2 1/k^{2} ) · 1983
Earlier work this paper cites.
In: Nonlinear Analysis and Optimization, pp. 102–126. Springer (1987)
Auslender, A.: Numerical methods for nondifferentiable convex optimization · 1987
Earlier work this paper cites.
Ph.D. thesis, Massachusetts Institute of Technology (1989)
Eckstein, J.: Splitting methods for monotone operators with applications to parallel optimization · 1989
Earlier work this paper cites.
Mathematical Programming 55
Eckstein, J., Bertsekas, D.P.: On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators · 1992
Earlier work this paper cites.
SIAM Journal on Optimization 2
Güler, O.: New proximal point algorithms for convex minimization · 1992
Earlier work this paper cites.
In: Advances in Optimization, pp. 39–51. Springer (1992)
Lemaire, B.: About the convergence of the proximal method · 1992
Earlier work this paper cites.
Mathematical Programming 62
Correa, R., Lemaréchal, C.: Convergence of some algorithms for convex minimization · 1993
Earlier work this paper cites.
In: 1995 Annual American Control Conference (ACC), vol. 4, pp. 2525–2526 (1995)
Toker, O., Ozbay, H.: On the np-hardness of solving bilinear matrix inequalities and simultaneous stabilization with static output feedback · 1995
Earlier work this paper cites.
Princeton University Press (1996)
Rockafellar, R.T.: Convex Analysis · 1996
Earlier work this paper cites.
Set-Valued Analysis 5
Burachik, R.S., Iusem, A.N., Svaiter, B.F.: Enlargement of monotone operators with applications to variational inequalities · 1997
Earlier work this paper cites.
Journal of Optimization Theory and Applications 95
Cominetti, R.: Coupling the proximal point algorithm with approximation methods · 1997
Earlier work this paper cites.
IEEE Transactions on Automatic Control 42
Megretski, A., Rantzer, A.: System analysis via integral quadratic constraints · 1997
Earlier work this paper cites.
In: Reformulation: nonsmooth, piecewise smooth, semismooth and smoothing methods, pp. 25–43. Springer (1998)
Burachik, R.S., Sagastizábal, C.A., Svaiter, B.: ε \varepsilon -enlargements of maximal monotone operators: Theory and applications · 1998
Earlier work this paper cites.
Mathematical programming 83
Eckstein, J.: Approximate iterations in bregman-function-based proximal algorithms · 1998
Earlier work this paper cites.
In: Ill-posed variational problems and regularization techniques, pp. 49–64. Springer (1999)
Burachik, R.S., Sagastizábal, C., Svaiter, B.: Bundle methods for maximal monotone operators · 1999
Earlier work this paper cites.
SIAM Journal on Control and Optimization 37
Burke, J., Qian, M.: A variable metric proximal point algorithm for monotone operators · 1999
Earlier work this paper cites.
Investigación Operativa 8
Iusem, A.N.: Augmented Lagrangian methods and proximal point methods for convex optimization · 1999
Earlier work this paper cites.
Set-Valued Analysis 7
Solodov, M.V., Svaiter, B.F.: A hybrid approximate extragradient–proximal point algorithm using the enlargement of a maximal monotone operator · 1999
Earlier work this paper cites.
Journal of Convex Analysis 6
Solodov, M.V., Svaiter, B.F.: A hybrid projection-proximal point algorithm · 1999
Earlier work this paper cites.
Optimization Methods and Software 11–12
Sturm, J.F.: Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones · 1999
Earlier work this paper cites.
In: Nonlinear optimization and related topics, pp. 415–427. Springer (2000)
Solodov, M.V., Svaiter, B.F.: A comparison of rates of convergence of two inexact proximal point algorithms · 2000
Cited alongside, same era.
Mathematical programming 88
Solodov, M.V., Svaiter, B.F.: Error bounds for proximal point subproblems and associated inexact proximal point algorithms · 2000
Cited alongside, same era.
Mathematics of Operations Research 25
Solodov, M.V., Svaiter, B.F.: An inexact hybrid generalized proximal point algorithm and some new results on the theory of Bregman functions · 2000
Cited alongside, same era.
Numerical functional analysis and optimization 22
Solodov, M.V., Svaiter, B.F.: A unified framework for some inexact proximal point algorithms · 2001
Cited alongside, same era.
In: Proceedings of the CACSD Conference (2004)
Löfberg, J.: YALMIP : A toolbox for modeling and optimization in MATLAB · 2004
Cited alongside, same era.
SIAM Journal on Optimization 15
Nemirovski, A.: Prox-method with rate of convergence o ( 1 / t ) o(1/t) for variational inequalities with lipschitz continuous monotone operators and smooth convex-concave saddle point problems · 2004
In: Proceedings of the 34th International Conference on Machine Learning-Volume 70, pp. 1549–1557. JMLR. org (2017)
Hu, B., Lessard, L.: Dissipativity theory for nesterov’s accelerated method · 2017
Later among the works it cites.
Optimization Letters 11
de Klerk, E., Glineur, F., Taylor, A.B.: On the worst-case complexity of the gradient method with exact line search for smooth strongly convex functions · 2017
Later among the works it cites.
SIAM Journal on Optimization 27
Taylor, A.B., Hendrickx, J.M., Glineur, F.: Exact worst-case performance of first-order methods for composite convex optimization · 2017
Later among the works it cites.
In: IEEE 56th Annual Conference on Decision and Control (CDC), pp. 1278–1283 (2017)
Taylor, A.B., Hendrickx, J.M., Glineur, F.: Performance Estimation Toolbox (PESTO): automated worst-case analysis of first-order optimization methods · 2017
Later among the works it cites.
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
Later among the works it cites.
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Cited alongside, same era.
SIAM Journal on Imaging Sciences 2
Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems · 2009
Cited alongside, same era.
SIAM Journal on Optimization 20
Monteiro, R.D., Svaiter, B.F.: On the complexity of the hybrid proximal extragradient method for the iterates and the ergodic mean · 2010
Cited alongside, same era.
Online at http://www.mosek.com 54
Mosek, A.: The MOSEK optimization software · 2010
Cited alongside, same era.
Springer (2011)
Bauschke, H.H., Combettes, P.L.: Convex analysis and monotone operator theory in Hilbert spaces, vol. 408 · 2011
Cited alongside, same era.
Foundations and Trends® in Machine learning 3
Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers · 2011
Cited alongside, same era.
In: Fixed-point algorithms for inverse problems in science and engineering, pp. 185–212. Springer (2011)
Combettes, P.L., Pesquet, J.C.: Proximal splitting methods in signal processing · 2011
Cited alongside, same era.
In: 2018 Annual American Control Conference (ACC), pp. 1376–1381 (2018)
Cyrus, S., Hu, B., Van Scoy, B., Lessard, L.: A robust accelerated optimization algorithm for strongly convex functions · 2018
Later among the works it cites.
Mathematical Programming 170
Eckstein, J., Yao, W.: Relative-error approximate versions of Douglas–Rachford splitting and special cases of the ADMM · 2018
Later among the works it cites.
SIAM Journal on Optimization 28
Kim, D., Fessler, J.A.: Another look at the fast iterative shrinkage/thresholding algorithm (fista) · 2018
Later among the works it cites.
Journal of Machine Learning Research 18
Lin, H., Mairal, J., Harchaoui, Z.: Catalyst acceleration for first-order convex optimization: from theory to practice · 2018
Later among the works it cites.
preprint arXiv:1809.02312 (2018)
Svaiter, B.F.: A weakly convergent fully inexact Douglas-Rachford method with relative error tolerance · 2018
Later among the works it cites.
IEEE Control Systems Letters 2
Van Scoy, B., Freeman, R.A., Lynch, K.M.: The fastest known globally convergent first-order method for minimizing strongly convex functions · 2018
Later among the works it cites.
Symmetry 10
Zong, C., Tang, Y., Cho, Y.: Convergence analysis of an inexact three-operator splitting algorithm · 2018
Later among the works it cites.
preprint arXiv:1904.10502 (2019)
Alves, M.M., Eckstein, J., Geremia, M., Melo, J.: Relative-error inertial-relaxed inexact versions of Douglas-Rachford and ADMM splitting algorithms · 2019
Later among the works it cites.
Set-Valued and Variational Analysis pp. 1–25 (2019)
Alves, M.M., Marcavillaca, R.T.: On inexact relative-error hybrid proximal extragradient, forward-backward and tseng’s modified forward-backward methods with inertial effects · 2019
Later among the works it cites.
IEEE Transactions on Signal Processing 67
Dixit, R., Bedi, A.S., Tripathi, R., Rajawat, K.: Online learning with inexact proximal online gradient descent algorithms · 2019
Later among the works it cites.
preprint arXiv:1905.06030 (2019)
Gu, G., Yang, J.: On the optimal ergodic sublinear convergence rate of the relaxed proximal point algorithm for variational inequalities · 2019
Later among the works it cites.
preprint arXiv:1904.05495 (2019)
Gu, G., Yang, J.: Optimal nonergodic sublinear convergence rate of proximal point algorithm for maximal monotone inclusion problems · 2019
Later among the works it cites.
Journal of Global Optimization 75
Millán, R.D., Machado, M.P.: Inexact proximal e p s i l o n epsilon -subgradient methods for composite convex optimization problems · 2019
Later among the works it cites.
preprint arXiv:1902.09788 (2019)
Ryu, E.K., Hannah, R., Yin, W.: Scaled relative graph: Nonexpansive operators via 2d euclidean geometry · 2019
Later among the works it cites.
Journal of Optimization Theory and Applications pp. 1–19 (2019)
Ryu, E.K., Vũ, B.C.: Finding the forward-Douglas–Rachford-forward method · 2019
Later among the works it cites.
In: Proceedings of the Thirty-Second Conference on Learning Theory (COLT), vol. 99, pp. 2934–2992. PMLR (2019)
Taylor, A., Bach, F.: Stochastic first-order methods: non-asymptotic and computer-aided analyses via potential functions · 2019
Later among the works it cites.
In: 2020 American Control Conference (ACC), pp. 2850–2857. IEEE (2020)
Ajalloeian, A., Simonetto, A., Dall’Anese, E.: Inexact online proximal-gradient method for time-varying convex optimization · 2020
Closest in time.
In: Conference on Learning Theory, pp. 452–478. PMLR (2020)
Barré, M., Taylor, A., d’Aspremont, A.: Complexity guarantees for polyak steps with momentum · 2020
Closest in time.
arXiv preprint arXiv:2001.00870 (2020)
Bastianello, N., Ajalloeian, A., Dall’Anese, E.: Distributed and inexact proximal gradient method for online convex optimization · 2020
Closest in time.
preprint arXiv:2005.03766 (2020)
Bello-Cruz, Y., Gonçalves, M.L.N., Krislock, N.: On inexact accelerated proximal gradient methods with relative error rules · 2020
Closest in time.
URL http://proximity-operator.net/download/guide.pdf
Chierchia, G., Chouzenoux, E., Combettes, P.L., Pesquet, J.C.: The proximity operator repository. user’s guide (2020) · 2020
Closest in time.
SIAM Journal on Optimization 30
De Klerk, E., Glineur, F., Taylor, A.B.: Worst-case convergence analysis of inexact gradient and newton methods through semidefinite programming performance estimation · 2020
Closest in time.
Mathematical Programming 184
Drori, Y., Taylor, A.B.: Efficient first-order methods for convex minimization: a constructive approach · 2020
Closest in time.
Optimization Letters pp. 1–14 (2020)
Lieder, F.: On the convergence rate of the halpern-iteration · 2020
Closest in time.
Tech. rep., CORE discussion paper (2020)
Nesterov, Y.: Inexact accelerated high-order proximal-point methods · 2020
Closest in time.
Tech. rep., CORE discussion paper (2020)
Nesterov, Y.: Inexact high-order proximal-point methods with auxiliary search procedure · 2020
Closest in time.
SIAM Journal on Optimization 30
Ryu, E.K., Taylor, A.B., Bergeling, C., Giselsson, P.: Operator splitting performance estimation: Tight contraction factors and optimal parameter selection · 2020
Closest in time.
Mathematical Programming pp. 1–43 (2021)
Dragomir, R.A., Taylor, A.B., d’Aspremont, A., Bolte, J.: Optimal complexity and certification of bregman first-order methods · 2021
Closest in time.
Mathematical Programming pp. 1–31 (2021)
Kim, D.: Accelerated proximal point method for maximally monotone operators · 2021
Closest in time.
Journal of Optimization Theory and Applications 188
Kim, D., Fessler, J.A.: Optimizing the efficiency of first-order methods for decreasing the gradient of smooth convex functions · 2021
Closest in time.