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Bauschke, Heinz H.

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Author ID: bauschke.heinz-h Recent zbMATH articles by "Bauschke, Heinz H."
Published as: Bauschke, Heinz H.; Bauschke, H. H.; Bauschke, Heinz; Bauschke, Heinz G.
External Links: MGP · ORCID
Documents Indexed: 145 Publications since 1993, including 5 Books
Reviewing Activity: 4 Reviews
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Serials

14 SIAM Journal on Optimization
10 Journal of Approximation Theory
10 Set-Valued and Variational Analysis
8 Mathematical Programming. Series A. Series B
8 Journal of Convex Analysis
5 Journal of Mathematical Analysis and Applications
5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
5 Proceedings of the American Mathematical Society
4 Journal of Optimization Theory and Applications
4 SIAM Journal on Control and Optimization
4 Optimization Letters
3 Mathematics of Operations Research
3 Transactions of the American Mathematical Society
3 Numerical Algorithms
3 Vietnam Journal of Mathematics
3 Journal of Nonlinear and Convex Analysis
2 Operations Research Letters
2 Optimization
2 Journal of Global Optimization
2 SIAM Review
2 Set-Valued Analysis
2 Foundations of Computational Mathematics
2 Pacific Journal of Optimization
2 CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC
2 Linear and Nonlinear Analysis
1 Applicable Analysis
1 Bulletin of the Australian Mathematical Society
1 Archiv der Mathematik
1 Canadian Journal of Mathematics
1 Journal of Functional Analysis
1 Operations Research
1 Pacific Journal of Mathematics
1 Linear Algebra and its Applications
1 Notices of the American Mathematical Society
1 Computational Optimization and Applications
1 Serdica Mathematical Journal
1 International Transactions in Operational Research
1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
1 Optimization Methods & Software
1 Communications in Contemporary Mathematics
1 Fixed Point Theory and Applications
1 Journal of Fixed Point Theory and Applications
1 ACM Communications in Computer Algebra
1 Springer Proceedings in Mathematics & Statistics
1 Pure and Applied Functional Analysis
1 Springer Optimization and Its Applications
1 Journal of Nonlinear and Variational Analysis

Publications by Year

Citations contained in zbMATH Open

131 Publications have been cited 4,002 times in 2,256 Documents Cited by Year
Convex analysis and monotone operator theory in Hilbert spaces. Zbl 1218.47001
Bauschke, Heinz H.; Combettes, Patrick L.
776
2011
On projection algorithms for solving convex feasibility problems. Zbl 0865.47039
Bauschke, Heinz H.; Borwein, Jonathan M.
609
1996
A weak-to-strong convergence principle for Fejér-monotone methods in Hilbert spaces. Zbl 1082.65058
Bauschke, Heinz H.; Combettes, Patrick L.
201
2001
The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space. Zbl 0956.47024
Bauschke, Heinz H.
190
1996
Convex analysis and monotone operator theory in Hilbert spaces. 2nd edition. Zbl 1359.26003
Bauschke, Heinz H.; Combettes, Patrick L.
169
2017
Projection and proximal point methods: Convergence results and counterexamples. Zbl 1059.47060
Bauschke, Heinz H.; Matoušková, Eva; Reich, Simeon
118
2004
Essential smoothness, essential strict convexity, and Legendre functions in Banach spaces. Zbl 1032.49025
Bauschke, Heinz H.; Borwein, Jonathan M.; Combettes, Patrick L.
108
2001
On the convergence of von Neumann’s alternating projection algorithm for two sets. Zbl 0801.47042
Bauschke, H. H.; Borwein, J. M.
90
1993
Bregman monotone optimization algorithms. Zbl 1049.90053
Bauschke, Heinz H.; Borwein, Jonathan M.; Combettes, Patrick L.
90
2003
Strong conical hull intersection property, bounded linear regularity, Jameson’s property \((G)\), and error bounds in convex optimization. Zbl 0998.90088
Bauschke, Heinz H.; Borwein, Jonathan M.; Li, Wu
83
1999
Legendre functions and the method of random Bregman projections. Zbl 0894.49019
Bauschke, Heinz G.; Borwein, Jonathan M.
82
1997
Finding best approximation pairs relative to two closed convex sets in Hilbert spaces. Zbl 1050.46021
Bauschke, Heinz H.; Combettes, Patrick L.; Luke, D. Russell
64
2004
The method of cyclic projections for closed convex sets in Hilbert space. Zbl 0874.47029
Bauschke, Heinz H.; Borwein, Jonathan M.; Lewis, Adrian S.
57
1997
Dykstra’s alternating projection algorithm for two sets. Zbl 0833.46011
Bauschke, H. H.; Borwein, J. M.
53
1994
A descent lemma beyond Lipschitz gradient continuity: first-order methods revisited and applications. Zbl 1364.90251
Bauschke, Heinz H.; Bolte, Jérôme; Teboulle, Marc
49
2017
The rate of linear convergence of the Douglas-Rachford algorithm for subspaces is the cosine of the Friedrichs angle. Zbl 1307.49030
Bauschke, Heinz H.; Bello Cruz, J. Y.; Nghia, Tran T. A.; Phan, Hung M.; Wang, Xianfu
41
2014
The asymptotic behavior of the composition of two resolvents. Zbl 1075.47033
Bauschke, Heinz H.; Combettes, Patrick L.; Reich, Simeon
36
2005
The proximal average: Basic theory. Zbl 1172.26003
Bauschke, Heinz H.; Goebel, Rafal; Lucet, Yves; Wang, Xianfu
34
2008
Linear and strong convergence of algorithms involving averaged nonexpansive operators. Zbl 1297.65060
Bauschke, Heinz H.; Noll, Dominikus; Phan, Hung M.
32
2015
Accelerating the convergence of the method of alternating projections. Zbl 1033.41019
Bauschke, Heinz H.; Deutsch, Frank; Hundal, Hein; Park, Sung-Ho
31
2003
Construction of best Bregman approximations in reflexive Banach spaces. Zbl 1040.41016
Bauschke, Heinz H.; Combettes, Patrick L.
30
2003
Extrapolation algorithm for affine-convex feasibility problems. Zbl 1098.65060
Bauschke, Heinz H.; Combettes, Patrick L.; Kruk, Serge G.
30
2006
Fitzpatrick functions, cyclic monotonicity and Rockafellar’s antiderivative. Zbl 1119.47050
Bartz, Sedi; Bauschke, Heinz H.; Borwein, Jonathan M.; Reich, Simeon; Wang, Xianfu
28
2007
Restricted normal cones and the method of alternating projections: theory. Zbl 1272.49027
Bauschke, Heinz H.; Luke, D. Russell; Phan, Hung M.; Wang, Xianfu
27
2013
Hyperbolic polynomials and convex analysis. Zbl 0974.90015
Bauschke, Heinz H.; Güler, Osman; Lewis, Adrian S.; Sendov, Hristo S.
26
2001
A new proximal point iteration that converges weakly but not in norm. Zbl 1071.65082
Bauschke, H. H.; Burke, J. V.; Deutsch, F. R.; Hundal, H. S.; Vanderwerff, J. D.
25
2005
On the Douglas-Rachford algorithm. Zbl 06751028
Bauschke, Heinz H.; Moursi, Walaa M.
25
2017
On the local convergence of the Douglas-Rachford algorithm. Zbl 1344.47044
Bauschke, H. H.; Noll, D.
23
2014
Fitzpatrick functions: inequalities, examples, and remarks on a problem by S. Fitzpatrick. Zbl 1117.26011
Bauschke, Heinz H.; McLaren, D. Alexander; Sendov, Hristo S.
22
2006
Fitzpatrick functions and continuous linear monotone operators. Zbl 1157.47034
Bauschke, Heinz H.; Borwein, Jonathan M.; Wang, Xianfu
22
2007
Dykstra’s algorithm with Bregman projections: A convergence proof. Zbl 0992.90052
Bauschke, Heinz H.; Lewis, Adrian S.
22
2000
Reflection-projection method for convex feasibility problems with an obtuse cone. Zbl 1136.90432
Bauschke, H. H.; Kruk, S. G.
21
2004
Attouch-Théra duality revisited: Paramonotonicity and operator splitting. Zbl 1254.47031
Bauschke, Heinz H.; Boţ, Radu I.; Hare, Warren L.; Moursi, Walaa M.
21
2012
The Douglas-Rachford algorithm for two (not necessarily intersecting) affine subspaces. Zbl 1341.47064
Bauschke, Heinz H.; Moursi, Walaa M.
20
2016
Bounded linear regularity, strong CHIP, and CHIP are distinct properties. Zbl 0964.90032
Bauschke, Heinz H.; Borwein, Jonathan M.; Tseng, Paul
20
2000
Firmly nonexpansive mappings and maximally monotone operators: correspondence and duality. Zbl 1263.47066
Bauschke, Heinz H.; Moffat, Sarah M.; Wang, Xianfu
20
2012
The kernel average for two convex functions and its application to the extension and representation of monotone operators. Zbl 1189.47051
Bauschke, Heinz H.; Wang, Xianfu
20
2009
Characterizing arbitrarily slow convergence in the method of alternating projections. Zbl 1208.47079
Bauschke, Heinz H.; Deutsch, Frank; Hundal, Hein
19
2009
A Dykstra-like algorithm for two monotone operators. Zbl 1176.47051
Bauschke, Heinz H.; Combettes, Patrick L.
19
2008
Projection methods: Swiss army knives for solving feasibility and best approximation problems with halfspaces. Zbl 1325.65080
Bauschke, Heinz H.; Koch, Valentin R.
19
2015
A strongly convergent reflection method for finding the projection onto the intersection of two closed convex sets in a Hilbert space. Zbl 1123.41021
Bauschke, Heinz H.; Combettes, Patrick L.; Luke, D. Russell
18
2006
Joint minimization with alternating Bregman proximity operators. Zbl 1124.90019
Bauschke, Heinz H.; Combettes, Patrick L.; Noll, Dominikus
18
2006
Restricted normal cones and the method of alternating projections: applications. Zbl 1349.65191
Bauschke, Heinz H.; Luke, D. Russell; Phan, Hung M.; Wang, Xianfu
18
2013
How to transform one convex function continuously into another. Zbl 1145.90050
Bauschke, Heinz H.; Lucet, Yves; Trienis, Michael
17
2008
Monotone linear relations: maximality and Fitzpatrick functions. Zbl 1193.47004
Bauschke, Heinz H.; Wang, Xianfu; Yao, Liangjin
17
2009
Restricted normal cones and sparsity optimization with affine constraints. Zbl 1298.49047
Bauschke, Heinz H.; Luke, D. Russell; Phan, Hung M.; Wang, Xianfu
16
2014
Fenchel duality, Fitzpatrick functions and the extension of firmly nonexpansive mappings. Zbl 1181.49017
Bauschke, Heinz H.
15
2007
Optimal rates of linear convergence of relaxed alternating projections and generalized Douglas-Rachford methods for two subspaces. Zbl 1351.65022
Bauschke, Heinz H.; Bello Cruz, Yunier Y.; Nghia, Tran T. A.; Pha, Hung M.; Wang, Xianfu
15
2016
A note on the paper by Eckstein and Svaiter on “general projective splitting methods for sums of maximal monotone operators”. Zbl 1197.47065
Bauschke, Heinz H.
15
2009
The Baillon-Haddad theorem revisited. Zbl 1208.47046
Bauschke, H. H.; Combettes, P. L.
14
2010
Proximal point algorithm, Douglas-Rachford algorithm and alternating projections: a case study. Zbl 1350.65057
Bauschke, Heinz H.; Dao, Minh N.; Noll, Dominikus; Phan, Hung M.
14
2016
Projection algorithms: Results and open problems. Zbl 0991.65050
Bauschke, Heinz H.
14
2001
A norm convergence result on random products of relaxed projections in Hilbert space. Zbl 0832.47055
Bauschke, H. H.
14
1995
The resolvent average for positive semidefinite matrices. Zbl 1191.15024
Bauschke, Heinz H.; Moffat, Sarah M.; Wang, Xianfu
14
2010
On Slater’s condition and finite convergence of the Douglas-Rachford algorithm for solving convex feasibility problems in Euclidean spaces. Zbl 1345.90065
Bauschke, Heinz H.; Dao, Minh N.; Noll, Dominikus; Phan, Hung M.
13
2016
The composition of projections onto closed convex sets in Hilbert space is asymptotically regular. Zbl 1016.47038
Bauschke, Heinz H.
13
2003
On the range of the Douglas-Rachford operator. Zbl 1350.47035
Bauschke, Heinz H.; Hare, Warren L.; Moursi, Walaa M.
12
2016
Maximal monotonicity of dense type, local maximal monotonicity, and monotonicity of the conjugate are all the same for continuous linear operators. Zbl 0932.47041
Bauschke, Heinz H.; Borwein, Jonathan M.
12
1999
Generalized solutions for the sum of two maximally monotone operators. Zbl 1297.47055
Bauschke, Heinz H.; Hare, Warren L.; Moursi, Walaa M.
12
2014
Fixed-point algorithms for inverse problems in science and engineering. Based on the presentations at the interdisciplinary workshop, BIRS, Banff, Canada, November 1–6, 2009. Zbl 1217.00018
Bauschke, Heinz H. (ed.); Burachik, Regina S. (ed.); Combettes, Patrick L. (ed.); Elser, Veit (ed.); Luke, D. Russell (ed.); Wolkowicz, Henry (ed.)
12
2011
On the finite convergence of the Douglas-Rachford algorithm for solving (not necessarily convex) feasibility problems in Euclidean spaces. Zbl 1365.90194
Bauschke, Heinz H.; Dao, Minh N.
12
2017
The Douglas-Rachford algorithm in the affine-convex case. Zbl 1408.90231
Bauschke, Heinz H.; Dao, Minh N.; Moursi, Walaa M.
11
2016
Primal-dual symmetric intrinsic methods for finding antiderivatives of cyclically monotone operators. Zbl 1189.47050
Bauschke, Heinz H.; Lucet, Yves; Wang, Xianfu
11
2007
Bregman distances and Chebyshev sets. Zbl 1175.49017
Bauschke, Heinz H.; Wang, Xianfu; Ye, Jane; Yuan, Xiaoming
10
2009
Autoconjugate representers for linear monotone operators. Zbl 1185.47050
Bauschke, Heinz H.; Wang, Xianfu; Yao, Liangjin
10
2010
On Borwein-Wiersma decompositions of monotone linear relations. Zbl 1215.47006
Bauschke, Heinz H.; Wang, Xianfu; Yao, Liangjin
10
2010
A projection method for approximating fixed points of quasi nonexpansive mappings without the usual demiclosedness condition. Zbl 1311.47085
Bauschke, Heinz H.; Chen, Jiawei; Wang, Xianfu
10
2014
The piecewise linear-quadratic model for computational convex analysis. Zbl 1186.90089
Lucet, Yves; Bauschke, Heinz H.; Trienis, Mike
10
2009
On subgradient projectors. Zbl 1316.47043
Bauschke, Heinz H.; Wang, Caifang; Wang, Xianfu; Xu, Jia
9
2015
On the order of the operators in the Douglas-Rachford algorithm. Zbl 1346.47015
Bauschke, Heinz H.; Moursi, Walaa M.
9
2016
Joint and separate convexity of the Bregman distance. Zbl 1160.65319
Bauschke, Heinz H.; Borwein, Jonathan M.
9
2001
Firmly nonexpansive and Kirszbraun-Valentine extensions: a constructive approach via monotone operator theory. Zbl 1247.47028
Bauschke, Heinz H.; Wang, Xianfu
9
2010
Compositions and convex combinations of asymptotically regular firmly nonexpansive mappings are also asymptotically regular. Zbl 1300.47056
Bauschke, Heinz H.; Martín-Márquez, Victoria; Moffat, Sarah M.; Wang, Xianfu
9
2012
Near equality, near convexity, sums of maximally monotone operators, and averages of firmly nonexpansive mappings. Zbl 1321.47113
Bauschke, Heinz H.; Moffat, Sarah M.; Wang, Xianfu
9
2013
The Brezis-Browder theorem in a general Banach space. Zbl 1259.47065
Bauschke, Heinz H.; Borwein, Jonathan M.; Wang, Xianfu; Yao, Liangjin
8
2012
An answer to S. Simons’ question on the maximal monotonicity of the sum of a maximal monotone linear operator and a normal cone operator. Zbl 1198.47070
Bauschke, Heinz H.; Wang, Xianfu; Yao, Liangjin
7
2009
Affine nonexpansive operators, Attouch-Théra duality and the Douglas-Rachford algorithm. Zbl 06804490
Bauschke, Heinz H.; Lukens, Brett; Moursi, Walaa M.
7
2017
The resolvent average of monotone operators: dominant and recessive properties. Zbl 1357.47053
Bartz, Sedi; Bauschke, Heinz H.; Moffat, Sarah M.; Wang, Xianfu
7
2016
Regularizing with Bregman-Moreau envelopes. Zbl 1409.90138
Bauschke, Heinz H.; Dao, Minh N.; Lindstrom, Scott B.
7
2018
Examples of discontinuous maximal monotone linear operators and the solution to a recent problem posed by B.F. Svaiter. Zbl 1197.47009
Bauschke, Heinz H.; Wang, Xianfu; Yao, Liangjin
7
2010
Symbolic computation of Fenchel conjugates. Zbl 1369.68356
Bauschke, Heinz H.; v. Mohrenschildt, Martin
7
2006
Iterating Bregman retractions. Zbl 1037.90048
Bauschke, Heinz H.; Combettes, Patrick L.
6
2003
On linear convergence of non-Euclidean gradient methods without strong convexity and Lipschitz gradient continuity. Zbl 1429.65121
Bauschke, Heinz H.; Bolte, Jérôme; Chen, Jiawei; Teboulle, Marc; Wang, Xianfu
6
2019
Chebyshev sets, Klee sets, and Chebyshev centers with respect to Bregman distances: recent results and open problems. Zbl 1251.41011
Bauschke, Heinz H.; Macklem, Mason S.; Wang, Xianfu
6
2011
New demiclosedness principles for (firmly) nonexpansive operators. Zbl 1297.47059
Bauschke, Heinz H.
6
2013
Every maximally monotone operator of Fitzpatrick-Phelps type is actually of dense type. Zbl 1319.90077
Bauschke, Heinz H.; Borwein, Jonathan M.; Wang, Xianfu; Yao, Liangjin
5
2012
Rectangularity and paramonotonicity of maximally monotone operators. Zbl 06315981
Bauschke, Heinz H.; Wang, Xianfu; Yao, Liangjin
5
2014
The method of alternating relaxed projections for two nonconvex sets. Zbl 1312.65092
Bauschke, Heinz H.; Phan, Hung M.; Wang, Xianfu
5
2014
Stadium norm and Douglas-Rachford splitting: a new approach to road design optimization. Zbl 1338.90381
Bauschke, Heinz H.; Koch, Valentin R.; Phan, Hung M.
5
2016
On the convexity of piecewise-defined functions. Zbl 1356.26005
Bauschke, Heinz H.; Lucet, Yves; Phan, Hung M.
5
2016
Compositions and averages of two resolvents: relative geometry of fixed points sets and a partial answer to a question by C. Byrne. Zbl 1228.47052
Wang, Xianfu; Bauschke, Heinz H.
5
2011
A convex-analytical approach to extension results for \(n\)-cyclically monotone operators. Zbl 1133.47037
Bauschke, Heinz H.; Wang, Xianfu
5
2007
An explicit example of a maximal 3-cyclically monotone operator with bizarre properties. Zbl 1170.47033
Bauschke, Heinz H.; Wang, Xianfu
4
2008
On Fejér monotone sequences and nonexpansive mappings. Zbl 1338.47060
Bauschke, Heinz H.; Dao, Minh N.; Moursi, Walaa M.
4
2015
The magnitude of the minimal displacement vector for compositions and convex combinations of firmly nonexpansive mappings. Zbl 1407.90341
Bauschke, Heinz H.; Moursi, Walaa M.
4
2018
Projecting onto the intersection of a cone and a sphere. Zbl 06913575
Bauschke, Heinz H.; Bui, Minh N.; Wang, Xianfu
4
2018
Bregman distances and Klee sets. Zbl 1172.52005
Bauschke, Heinz H.; Wang, Xianfu; Ye, Jane; Yuan, Xiaoming
4
2009
Conical open mapping theorems and regularity. Zbl 1193.90167
Bauschke, Heinz H.; Borwein, Jonathan M.
4
1999
Fixed points of averages of resolvents: geometry and algorithms. Zbl 1263.47064
Bauschke, Heinz H.; Wang, Xianfu; Wylie, Calvin J. S.
4
2012
On the maximal monotonicity of the sum of a maximal monotone linear relation and the subdifferential operator of a sublinear function. Zbl 1272.47067
Bauschke, Heinz H.; Wang, Xianfu; Yao, Liangjin
4
2012
On the linear convergence of circumcentered isometry methods. Zbl 07340125
Bauschke, Heinz H.; Ouyang, Hui; Wang, Xianfu
1
2021
Resolvents and Yosida approximations of displacement mappings of isometries. Zbl 07383628
Alwadani, Salihah; Bauschke, Heinz H.; Revalski, Julian P.; Wang, Xianfu
1
2021
On the behavior of the Douglas-Rachford algorithm for minimizing a convex function subject to a linear constraint. Zbl 1451.90117
Bauschke, Heinz H.; Moursi, Walaa M.
1
2020
On the minimal displacement vector of compositions and convex combinations of nonexpansive mappings. Zbl 07290668
Bauschke, Heinz H.; Moursi, Walaa M.
1
2020
Circumcentered methods induced by isometries. Zbl 07341166
Bauschke, Heinz H.; Ouyang, Hui; Wang, Xianfu
1
2020
On linear convergence of non-Euclidean gradient methods without strong convexity and Lipschitz gradient continuity. Zbl 1429.65121
Bauschke, Heinz H.; Bolte, Jérôme; Chen, Jiawei; Teboulle, Marc; Wang, Xianfu
6
2019
The Douglas-Rachford algorithm for a hyperplane and a doubleton. Zbl 07069295
Bauschke, Heinz H.; Dao, Minh N.; Lindstrom, Scott B.
2
2019
On sums and convex combinations of projectors onto convex sets. Zbl 07050069
Bauschke, Heinz H.; Bui, Minh N.; Wang, Xianfu
1
2019
Regularizing with Bregman-Moreau envelopes. Zbl 1409.90138
Bauschke, Heinz H.; Dao, Minh N.; Lindstrom, Scott B.
7
2018
The magnitude of the minimal displacement vector for compositions and convex combinations of firmly nonexpansive mappings. Zbl 1407.90341
Bauschke, Heinz H.; Moursi, Walaa M.
4
2018
Projecting onto the intersection of a cone and a sphere. Zbl 06913575
Bauschke, Heinz H.; Bui, Minh N.; Wang, Xianfu
4
2018
On the asymptotic behaviour of the Aragón Artacho-Campoy algorithm. Zbl 07165733
Alwadani, Salihah; Bauschke, Heinz H.; Moursi, Walaa M.; Wang, Xianfu
3
2018
On circumcenters of finite sets in Hilbert spaces. Zbl 1456.51008
Bauschke, Heinz H.; Ouyang, Hui; Wang, Xianfu
3
2018
On Douglas-Rachford operators that fail to be proximal mappings. Zbl 06857151
Bauschke, Heinz H.; Schaad, Jason; Wang, Xianfu
2
2018
A class of multi-marginal \(c\)-cyclically monotone sets with explicit \(c\)-splitting potentials. Zbl 1386.49034
Bartz, Sedi; Bauschke, Heinz H.; Wang, Xianfu
1
2018
Subgradient projectors: extensions, theory, and characterizations. Zbl 1422.49014
Bauschke, Heinz H.; Wang, Caifang; Wang, Xianfu; Xu, Jia
1
2018
Convex analysis and monotone operator theory in Hilbert spaces. 2nd edition. Zbl 1359.26003
Bauschke, Heinz H.; Combettes, Patrick L.
169
2017
A descent lemma beyond Lipschitz gradient continuity: first-order methods revisited and applications. Zbl 1364.90251
Bauschke, Heinz H.; Bolte, Jérôme; Teboulle, Marc
49
2017
On the Douglas-Rachford algorithm. Zbl 06751028
Bauschke, Heinz H.; Moursi, Walaa M.
25
2017
On the finite convergence of the Douglas-Rachford algorithm for solving (not necessarily convex) feasibility problems in Euclidean spaces. Zbl 1365.90194
Bauschke, Heinz H.; Dao, Minh N.
12
2017
Affine nonexpansive operators, Attouch-Théra duality and the Douglas-Rachford algorithm. Zbl 06804490
Bauschke, Heinz H.; Lukens, Brett; Moursi, Walaa M.
7
2017
The resolvent order: a unification of the orders by Zarantonello, by Loewner, and by Moreau. Zbl 1425.47006
Bartz, Sedi; Bauschke, Heinz H.; Wang, Xianfu
2
2017
The Douglas-Rachford algorithm for two (not necessarily intersecting) affine subspaces. Zbl 1341.47064
Bauschke, Heinz H.; Moursi, Walaa M.
20
2016
Optimal rates of linear convergence of relaxed alternating projections and generalized Douglas-Rachford methods for two subspaces. Zbl 1351.65022
Bauschke, Heinz H.; Bello Cruz, Yunier Y.; Nghia, Tran T. A.; Pha, Hung M.; Wang, Xianfu
15
2016
Proximal point algorithm, Douglas-Rachford algorithm and alternating projections: a case study. Zbl 1350.65057
Bauschke, Heinz H.; Dao, Minh N.; Noll, Dominikus; Phan, Hung M.
14
2016
On Slater’s condition and finite convergence of the Douglas-Rachford algorithm for solving convex feasibility problems in Euclidean spaces. Zbl 1345.90065
Bauschke, Heinz H.; Dao, Minh N.; Noll, Dominikus; Phan, Hung M.
13
2016
On the range of the Douglas-Rachford operator. Zbl 1350.47035
Bauschke, Heinz H.; Hare, Warren L.; Moursi, Walaa M.
12
2016
The Douglas-Rachford algorithm in the affine-convex case. Zbl 1408.90231
Bauschke, Heinz H.; Dao, Minh N.; Moursi, Walaa M.
11
2016
On the order of the operators in the Douglas-Rachford algorithm. Zbl 1346.47015
Bauschke, Heinz H.; Moursi, Walaa M.
9
2016
The resolvent average of monotone operators: dominant and recessive properties. Zbl 1357.47053
Bartz, Sedi; Bauschke, Heinz H.; Moffat, Sarah M.; Wang, Xianfu
7
2016
Stadium norm and Douglas-Rachford splitting: a new approach to road design optimization. Zbl 1338.90381
Bauschke, Heinz H.; Koch, Valentin R.; Phan, Hung M.
5
2016
On the convexity of piecewise-defined functions. Zbl 1356.26005
Bauschke, Heinz H.; Lucet, Yves; Phan, Hung M.
5
2016
On a result of Pazy concerning the asymptotic behaviour of nonexpansive mappings. Zbl 1387.47030
Bauschke, Heinz H.; Douglas, Graeme R.; Moursi, Walaa M.
2
2016
Linear and strong convergence of algorithms involving averaged nonexpansive operators. Zbl 1297.65060
Bauschke, Heinz H.; Noll, Dominikus; Phan, Hung M.
32
2015
Projection methods: Swiss army knives for solving feasibility and best approximation problems with halfspaces. Zbl 1325.65080
Bauschke, Heinz H.; Koch, Valentin R.
19
2015
On subgradient projectors. Zbl 1316.47043
Bauschke, Heinz H.; Wang, Caifang; Wang, Xianfu; Xu, Jia
9
2015
On Fejér monotone sequences and nonexpansive mappings. Zbl 1338.47060
Bauschke, Heinz H.; Dao, Minh N.; Moursi, Walaa M.
4
2015
On the finite convergence of a projected cutter method. Zbl 1353.90108
Bauschke, Heinz H.; Wang, Caifang; Wang, Xianfu; Xu, Jia
3
2015
A Bregman projection method for approximating fixed points of quasi-Bregman nonexpansive mappings. Zbl 1309.47070
Bauschke, Heinz H.; Chen, Jiawei; Wang, Xianfu
3
2015
A derivative-free comirror algorithm for convex optimization. Zbl 1328.90104
Bauschke, Heinz H.; Hare, Warren L.; Moursi, Walaa M.
3
2015
The rate of linear convergence of the Douglas-Rachford algorithm for subspaces is the cosine of the Friedrichs angle. Zbl 1307.49030
Bauschke, Heinz H.; Bello Cruz, J. Y.; Nghia, Tran T. A.; Phan, Hung M.; Wang, Xianfu
41
2014
On the local convergence of the Douglas-Rachford algorithm. Zbl 1344.47044
Bauschke, H. H.; Noll, D.
23
2014
Restricted normal cones and sparsity optimization with affine constraints. Zbl 1298.49047
Bauschke, Heinz H.; Luke, D. Russell; Phan, Hung M.; Wang, Xianfu
16
2014
Generalized solutions for the sum of two maximally monotone operators. Zbl 1297.47055
Bauschke, Heinz H.; Hare, Warren L.; Moursi, Walaa M.
12
2014
A projection method for approximating fixed points of quasi nonexpansive mappings without the usual demiclosedness condition. Zbl 1311.47085
Bauschke, Heinz H.; Chen, Jiawei; Wang, Xianfu
10
2014
Rectangularity and paramonotonicity of maximally monotone operators. Zbl 06315981
Bauschke, Heinz H.; Wang, Xianfu; Yao, Liangjin
5
2014
The method of alternating relaxed projections for two nonconvex sets. Zbl 1312.65092
Bauschke, Heinz H.; Phan, Hung M.; Wang, Xianfu
5
2014
On moving averages. Zbl 1320.15031
Bauschke, Heinz H.; Sarada, Joshua; Wang, Xianfu
1
2014
The method of cyclic intrepid projections: convergence analysis and numerical experiments. Zbl 1326.65065
Bauschke, Heinz H.; Iorio, Francesco; Koch, Valentin R.
1
2014
Restricted normal cones and the method of alternating projections: theory. Zbl 1272.49027
Bauschke, Heinz H.; Luke, D. Russell; Phan, Hung M.; Wang, Xianfu
27
2013
Restricted normal cones and the method of alternating projections: applications. Zbl 1349.65191
Bauschke, Heinz H.; Luke, D. Russell; Phan, Hung M.; Wang, Xianfu
18
2013
Near equality, near convexity, sums of maximally monotone operators, and averages of firmly nonexpansive mappings. Zbl 1321.47113
Bauschke, Heinz H.; Moffat, Sarah M.; Wang, Xianfu
9
2013
New demiclosedness principles for (firmly) nonexpansive operators. Zbl 1297.47059
Bauschke, Heinz H.
6
2013
On cluster points of alternating projections. Zbl 1324.65095
Bauschke, Heinz H.; Noll, Dominikus
3
2013
Computational and analytical mathematics. In Honor of Jonathan Borwein’s 60th birthday. Selected papers based on the presentations at the workshop, also known as JonFest, Simon Fraser University, BC, Canada, May 16–20, 2011. Zbl 1276.00018
Bailey, David H.; Bauschke, Heinz H.; Borwein, Peter; Garvan, Frank; Théra, Michel; Vanderwerff, Jon D.; Wolkowicz, Henry
1
2013
Attouch-Théra duality revisited: Paramonotonicity and operator splitting. Zbl 1254.47031
Bauschke, Heinz H.; Boţ, Radu I.; Hare, Warren L.; Moursi, Walaa M.
21
2012
Firmly nonexpansive mappings and maximally monotone operators: correspondence and duality. Zbl 1263.47066
Bauschke, Heinz H.; Moffat, Sarah M.; Wang, Xianfu
20
2012
Compositions and convex combinations of asymptotically regular firmly nonexpansive mappings are also asymptotically regular. Zbl 1300.47056
Bauschke, Heinz H.; Martín-Márquez, Victoria; Moffat, Sarah M.; Wang, Xianfu
9
2012
The Brezis-Browder theorem in a general Banach space. Zbl 1259.47065
Bauschke, Heinz H.; Borwein, Jonathan M.; Wang, Xianfu; Yao, Liangjin
8
2012
Every maximally monotone operator of Fitzpatrick-Phelps type is actually of dense type. Zbl 1319.90077
Bauschke, Heinz H.; Borwein, Jonathan M.; Wang, Xianfu; Yao, Liangjin
5
2012
Fixed points of averages of resolvents: geometry and algorithms. Zbl 1263.47064
Bauschke, Heinz H.; Wang, Xianfu; Wylie, Calvin J. S.
4
2012
On the maximal monotonicity of the sum of a maximal monotone linear relation and the subdifferential operator of a sublinear function. Zbl 1272.47067
Bauschke, Heinz H.; Wang, Xianfu; Yao, Liangjin
4
2012
Construction of pathological maximally monotone operators on non-reflexive Banach spaces. Zbl 1267.47003
Bauschke, Heinz H.; Borwein, Jonathan M.; Wang, Xianfu; Yao, Liangjin
3
2012
What is…a Fenchel conjugate? Zbl 1248.49047
Bauschke, Heinz H.; Lucet, Yves
2
2012
Convex analysis and monotone operator theory in Hilbert spaces. Zbl 1218.47001
Bauschke, Heinz H.; Combettes, Patrick L.
776
2011
Fixed-point algorithms for inverse problems in science and engineering. Based on the presentations at the interdisciplinary workshop, BIRS, Banff, Canada, November 1–6, 2009. Zbl 1217.00018
Bauschke, Heinz H.; Burachik, Regina S.; Combettes, Patrick L.; Elser, Veit; Luke, D. Russell; Wolkowicz, Henry
12
2011
Chebyshev sets, Klee sets, and Chebyshev centers with respect to Bregman distances: recent results and open problems. Zbl 1251.41011
Bauschke, Heinz H.; Macklem, Mason S.; Wang, Xianfu
6
2011
Compositions and averages of two resolvents: relative geometry of fixed points sets and a partial answer to a question by C. Byrne. Zbl 1228.47052
Wang, Xianfu; Bauschke, Heinz H.
5
2011
Self-dual smooth approximations of convex functions via the proximal average. Zbl 1250.26015
Bauschke, Heinz H.; Moffat, Sarah M.; Wang, Xianfu
2
2011
The Baillon-Haddad theorem revisited. Zbl 1208.47046
Bauschke, H. H.; Combettes, P. L.
14
2010
The resolvent average for positive semidefinite matrices. Zbl 1191.15024
Bauschke, Heinz H.; Moffat, Sarah M.; Wang, Xianfu
14
2010
Autoconjugate representers for linear monotone operators. Zbl 1185.47050
Bauschke, Heinz H.; Wang, Xianfu; Yao, Liangjin
10
2010
On Borwein-Wiersma decompositions of monotone linear relations. Zbl 1215.47006
Bauschke, Heinz H.; Wang, Xianfu; Yao, Liangjin
10
2010
Firmly nonexpansive and Kirszbraun-Valentine extensions: a constructive approach via monotone operator theory. Zbl 1247.47028
Bauschke, Heinz H.; Wang, Xianfu
9
2010
Examples of discontinuous maximal monotone linear operators and the solution to a recent problem posed by B.F. Svaiter. Zbl 1197.47009
Bauschke, Heinz H.; Wang, Xianfu; Yao, Liangjin
7
2010
Klee sets and Chebyshev centers for the right Bregman distance. Zbl 1200.52006
Bauschke, Heinz H.; Macklem, Mason S.; Sewell, Jason B.; Wang, Xianfu
1
2010
The kernel average for two convex functions and its application to the extension and representation of monotone operators. Zbl 1189.47051
Bauschke, Heinz H.; Wang, Xianfu
20
2009
Characterizing arbitrarily slow convergence in the method of alternating projections. Zbl 1208.47079
Bauschke, Heinz H.; Deutsch, Frank; Hundal, Hein
19
2009
Monotone linear relations: maximality and Fitzpatrick functions. Zbl 1193.47004
Bauschke, Heinz H.; Wang, Xianfu; Yao, Liangjin
17
2009
A note on the paper by Eckstein and Svaiter on “general projective splitting methods for sums of maximal monotone operators”. Zbl 1197.47065
Bauschke, Heinz H.
15
2009
Bregman distances and Chebyshev sets. Zbl 1175.49017
Bauschke, Heinz H.; Wang, Xianfu; Ye, Jane; Yuan, Xiaoming
10
2009
The piecewise linear-quadratic model for computational convex analysis. Zbl 1186.90089
Lucet, Yves; Bauschke, Heinz H.; Trienis, Mike
10
2009
An answer to S. Simons’ question on the maximal monotonicity of the sum of a maximal monotone linear operator and a normal cone operator. Zbl 1198.47070
Bauschke, Heinz H.; Wang, Xianfu; Yao, Liangjin
7
2009
Bregman distances and Klee sets. Zbl 1172.52005
Bauschke, Heinz H.; Wang, Xianfu; Ye, Jane; Yuan, Xiaoming
4
2009
The proximal average: Basic theory. Zbl 1172.26003
Bauschke, Heinz H.; Goebel, Rafal; Lucet, Yves; Wang, Xianfu
34
2008
A Dykstra-like algorithm for two monotone operators. Zbl 1176.47051
Bauschke, Heinz H.; Combettes, Patrick L.
19
2008
How to transform one convex function continuously into another. Zbl 1145.90050
Bauschke, Heinz H.; Lucet, Yves; Trienis, Michael
17
2008
An explicit example of a maximal 3-cyclically monotone operator with bizarre properties. Zbl 1170.47033
Bauschke, Heinz H.; Wang, Xianfu
4
2008
Fitzpatrick functions, cyclic monotonicity and Rockafellar’s antiderivative. Zbl 1119.47050
Bartz, Sedi; Bauschke, Heinz H.; Borwein, Jonathan M.; Reich, Simeon; Wang, Xianfu
28
2007
Fitzpatrick functions and continuous linear monotone operators. Zbl 1157.47034
Bauschke, Heinz H.; Borwein, Jonathan M.; Wang, Xianfu
22
2007
Fenchel duality, Fitzpatrick functions and the extension of firmly nonexpansive mappings. Zbl 1181.49017
Bauschke, Heinz H.
15
2007
Primal-dual symmetric intrinsic methods for finding antiderivatives of cyclically monotone operators. Zbl 1189.47050
Bauschke, Heinz H.; Lucet, Yves; Wang, Xianfu
11
2007
A convex-analytical approach to extension results for \(n\)-cyclically monotone operators. Zbl 1133.47037
Bauschke, Heinz H.; Wang, Xianfu
5
2007
Extrapolation algorithm for affine-convex feasibility problems. Zbl 1098.65060
Bauschke, Heinz H.; Combettes, Patrick L.; Kruk, Serge G.
30
2006
Fitzpatrick functions: inequalities, examples, and remarks on a problem by S. Fitzpatrick. Zbl 1117.26011
Bauschke, Heinz H.; McLaren, D. Alexander; Sendov, Hristo S.
22
2006
A strongly convergent reflection method for finding the projection onto the intersection of two closed convex sets in a Hilbert space. Zbl 1123.41021
Bauschke, Heinz H.; Combettes, Patrick L.; Luke, D. Russell
18
2006
Joint minimization with alternating Bregman proximity operators. Zbl 1124.90019
Bauschke, Heinz H.; Combettes, Patrick L.; Noll, Dominikus
18
2006
Symbolic computation of Fenchel conjugates. Zbl 1369.68356
Bauschke, Heinz H.; v. Mohrenschildt, Martin
7
2006
The asymptotic behavior of the composition of two resolvents. Zbl 1075.47033
Bauschke, Heinz H.; Combettes, Patrick L.; Reich, Simeon
36
2005
A new proximal point iteration that converges weakly but not in norm. Zbl 1071.65082
Bauschke, H. H.; Burke, J. V.; Deutsch, F. R.; Hundal, H. S.; Vanderwerff, J. D.
25
2005
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Cited by 2,160 Authors

83 Bauschke, Heinz H.
54 Reich, Simeon
54 Wang, Shawn Xianfu
48 Boţ, Radu Ioan
44 Combettes, Patrick L.
39 Yao, Yonghong
38 Yao, Jen-Chih
35 Censor, Yair
34 Csetnek, Ernö Robert
33 Shehu, Yekini
32 Cho, Yeol Je
32 Dong, Qiaoli
31 Liou, Yeongcheng
29 Borwein, Jonathan Michael
27 Attouch, Hedy
26 Zegeye, Habtu
25 Iiduka, Hideaki
24 He, Songnian
23 Gibali, Aviv
23 Zaslavski, Alexander Yakovlevich
22 Dang Van Hieu
22 Kang, Shin Min
22 Qin, Xiaolong
22 Tam, Matthew K.
21 Cholamjiak, Prasit
21 Kumam, Poom
20 Mewomo, Oluwatosin Temitope
20 Suantai, Suthep
19 Luke, D. Russell
18 Cegielski, Andrzej
18 Shahzad, Naseer
18 Tang, Yuchao
17 Moursi, Walaa M.
17 Phan, Hung M.
16 Trương Minh Tuyên
16 Yao, Liangjin
15 Chidume, Charles Ejike
15 Peyré, Gabriel
15 Wang, Fenghui
15 Xu, Hong-Kun
15 Yamada, Isao
15 Yuan, Xiaoming
14 Aragón Artacho, Francisco Javier
14 Bello Cruz, Jose Yunier
14 Dang, Yazheng
14 Maingé, Paul-Emile
14 Zhou, Haiyun
13 Briceño-Arias, Luis M.
13 Chang, Shih-Sen
13 Dao, Minh Ngoc
13 Deutsch, Frank
13 Iyiola, Olaniyi Samuel
13 Kruger, Alexander Ya.
13 Marino, Giuseppe
13 Peypouquet, Juan
13 Zhao, Jing
12 Ceng, Lu-Chuan
12 Han, Deren
12 Jolaoso, Lateef Olakunle
12 Kanzow, Christian
12 Mordukhovich, Boris S.
12 Pesquet, Jean-Christophe
12 Shen, Lixin
12 Vũ, Bằng Công
12 Xu, Yuesheng
12 Zalas, Rafał
11 Ali, Bashir
11 Fadili, Jalal M.
11 Hundal, Hein S.
11 Li, Guoyin
11 Lim, Yongdo
11 Tran Dinh Quoc
11 Ugwunnadi, Godwin Chidi
10 Chen, Rudong
10 Clason, Christian
10 Gao, Yan
10 Izuchukwu, Chinedu
10 Naraghirad, Eskandar
10 Peng, Jigen
10 Sahu, Daya Ram
10 Thao, Nguyen Hieu
10 Vuong, Phan Tu
10 Yin, Wotao
9 Cabot, Alexandre
9 Cholamjiak, Watcharaporn
9 Li, Chong
9 Liu, Liwei
9 Lucet, Yves
9 Mohebi, Hossein
9 Nakajo, Kazuhide
9 Rassias, Themistocles Michael
9 Sabach, Shoham
9 Strodiot, Jean-Jacques
9 Takahashi, Wataru
9 Villa, Silvia
8 Burachik, Regina Sandra
8 Campoy, Rubén
8 Ferreira, Orizon Pereira
8 Kim, Jong Kyu
8 López Acedo, Genaro
...and 2,060 more Authors
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Cited in 299 Serials

144 Journal of Optimization Theory and Applications
113 SIAM Journal on Optimization
103 Fixed Point Theory and Applications
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6 Rendiconti del Circolo Matemàtico di Palermo. Serie II
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