Fetching the paper…
Reading the bibliography…
Moreau's seminal paper, introducing what is now called the Moreau envelope and the proximity operator (also known as the proximal mapping), appeared in 1965.
J.-J. Moreau, Fonctions convexes duales et points proximaux dans un espace hilbertien, Comptes Rendus de l’Académie des Sciences 255 (1962), 2897–2899
1962
Earlier work this paper cites.
J.-J. Moreau, Proximité et dualité dans un espace hilbertien, Bulletin de la Société Mathématique de France 93 (1965), 273–299
1965
Earlier work this paper cites.
L.M. Bregman, The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming, USSR Computational Mathematics and Mathematical Physics 7 (1967), 200–217
1967
Earlier work this paper cites.
R.T. Rockafellar, Convex Analysis , Princeton University Press, 1970
1970
Earlier work this paper cites.
H. Attouch, Convergence de fonctions convexes, des sous-différentiels et semi-groupes associés, Comptes Rendus de l’Académie des Sciences de Paris 284 (1977), 539–542
1977
Earlier work this paper cites.
H. Attouch, Variational Convergence for Functions and Operators , Pitman, 1984
1984
Earlier work this paper cites.
J.M. Borwein and A.S. Lewis, Duality relationships for entropy–like minimization problems, SIAM Journal on Control and Optimization 29 (1991), 325–338
1991
Earlier work this paper cites.
Y. Censor and S.A. Zenios, Proximal minimization algorithm with D-functions, Journal of Optimization Theory and Applications 73 (1992), 451–464
1992
Earlier work this paper cites.
G. Chen and M. Teboulle, Convergence analysis of a proximal-like minimization algorithm using Bregman functions, SIAM Journal on Optimization 3 (1993), 538–543
1993
Earlier work this paper cites.
J. Eckstein, Nonlinear proximal point algorithms using Bregman functions, with applications to convex programming, Mathematics of Operations Research 18 (1993), 202–226
1993
Earlier work this paper cites.
J.-B. Hiriart-Urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms II: Advanced Theory and Bundle Methods , Springer, 1993
1993
Earlier work this paper cites.
H.H. Bauschke and J.M. Borwein, Legendre functions and the method of random Bregman projections, Journal of Convex Analysis 4 (1997), 27–67
1997
Earlier work this paper cites.
Y. Censor and S.A. Zenios, Parallel Optimization: Theory, Algorithms, and Applications , Oxford University Press, 1997
1997
Earlier work this paper cites.
K.C. Kiwiel, Proximal minimization methods with generalized Bregman functions, SIAM Journal on Control and Optimization 35 (1997), 1142–1168
1997
Earlier work this paper cites.
Y. Censor and S. Reich, The Dykstra algorithm with Bregman projections, Communications in Applied Analysis 2 (1998), 407–419
1998
Earlier work this paper cites.
R.T. Rockafellar and R.J-B Wets, Variational Analysis , Springer-Verlag, 1998
1998
Cited alongside, same era.
H.H. Bauschke and A.S. Lewis, Dykstra’s algorithm with Bregman projectors: a convergence proof, Optimization 48 (2000), 409–427
2000
Cited alongside, same era.
D. Butnariu and A.N. Iusem, Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization , Kluwer, 2000
2000
Cited alongside, same era.
C. Byrne and Y. Censor, Proximity function minimization using multiple Bregman projections, with applications to split feasibility and Kullback–Leibler distance minimization, Annals of Operations Research 105 (2001), 77–98
2001
Cited alongside, same era.
H.H. Bauschke and D. Noll, The method of forward projections, Journal of Nonlinear and Convex Analysis 3 (2002), 191–205
2002
Cited alongside, same era.
R. Burachik and G. Kassay, On a generalized proximal point method for solving equilibrium problems in Banach spaces, Nonlinear Analysis 75 (2012), 6456–6464
2012
Later among the works it cites.
Y.Y. Chen, C. Kan, and W. Song, The Moreau envelop function and proximal mapping with respect to the Bregman distance in Banach spaces, Vietnam Journal of Mathematics 40 (2012), 181–199
2012
Later among the works it cites.
C. Kan and W. Song, The Moreau envelope function and proximal mapping in the sense of the Bregman distance, Nonlinear Analysis 75 (2012), 1385–1399
2012
Later among the works it cites.
P.L. Combettes and N.N. Reyes, Moreau’s decomposition in Banach spaces, Mathematical Programming , 139 (2013), 103–114
2013
Later among the works it cites.
B.S. Mordukhovich and N.M. Nam, An Easy Path to Convex Analysis and Applications , Morgan & Claypool Publishers, 2013
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Y. Censor and G. T. Herman, Block-iterative algorithms with underrelaxed Bregman projections, SIAM Journal on Optimization 13 (2002), 283–297
2002
Cited alongside, same era.
H.H. Bauschke, J.M. Borwein, and P.L. Combettes, Bregman monotone optimization algorithms, SIAM Journal on Control and Optimization 42 (2003), 596–636
2003
Cited alongside, same era.
H.H. Bauschke and P.L. Combettes, Iterating Bregman retractions, SIAM Journal on Optimization 13 (2003), 1159–1173
2003
Cited alongside, same era.
J.M. Borwein and Q. Zhu, Techniques of Variational Analysis , Springer, 2005
2005
Cited alongside, same era.
H.H. Bauschke, P.L. Combettes, and D. Noll, Joint minimization with alternating Bregman proximity operators, Pacific Journal of Optimization 2 (2006), 401–424
2006
Cited alongside, same era.
J.M. Borwein and A.S. Lewis, Convex Analysis and Nonlinear Optimization: Theory and Examples , second edition Springer, 2006
2006
Cited alongside, same era.
J.M. Borwein and J. D. Vanderwerff, Convex Functions: Constructions, Characterizations and Counterexamples , Cambridge University Press, 2010
2010
Cited alongside, same era.
2013
Later among the works it cites.
J.M. Borwein and L. Yao, Legendre-type integrands and convex integral functions, Journal of Convex Analysis 21 (2014), 264–288
2014
Later among the works it cites.
H.H. Bauschke, J. Bolte, and M. Teboulle, A descent lemma beyond Lipschitz gradient continuity: first-order methods revisited and applications, Mathematics of Operations Research 42 (2016), 330–348
2016
Later among the works it cites.
P.L. Combettes and Q.V. Nguyen, Solving composite monotone inclusions in reflexive Banach spaces by constructing best Bregman approximations from their Kuhn–Tucker set, Journal of Convex Analysis 23 (2016), 481–510
2016
Later among the works it cites.
K. Lange, MM Optimization Algorithms , SIAM, 2016
2016
Later among the works it cites.
Q.V. Nguyen, Variable quasi-Bregman monotone sequences, Numerical Algorithms 73 (2016), 1107–1130
2016
Later among the works it cites.
F. Alvarez, R. Correa, and M. Marechal, Regular self-proximal distances are Bregman, Journal of Convex Analysis 24 (2017), 135–148
2017
Closest in time.
H.H. Bauschke and P.L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces , second edition, Springer, 2017
2017
Closest in time.
J.M. Borwein and S.B. Lindstrom, Meetings with Lambert 𝒲 \mathcal{W} and other special functions in optimization and analysis, Pure and Applied Functional Analysis 1(3) (2017), 361–396
2017
Closest in time.
Q.V. Nguyen, Forward-backward splitting with Bregman distances, Vietnam Journal of Mathematics 45 (2017), 519–539
2017
Closest in time.