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Preface: Special Issue in Honor of the 60th Birthday of Sylvain Sorin
Asymptotic behavior of compositions of under-relaxed nonexpansive operators
1. | Université Paris 1 Panthéon-Sorbonne, SAMM – EA 4543, 75013 Paris, France |
2. | Sorbonne Universités – UPMC Univ. Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France |
3. | Universidad de Chile, Departamento de Ingeniería Industrial, Santiago, Chile |
References:
[1] |
H. Attouch, L. M. Briceño-Arias and P. L. Combettes, A parallel splitting method for coupled monotone inclusions, SIAM J. Control Optim., 48 (2010), 3246-3270.
doi: 10.1137/090754297. |
[2] |
J.-B. Baillon, P. L. Combettes and R. Cominetti, There is no variational characterization of the cycles in the method of periodic projections, J. Funct. Anal., 262 (2012), 400-408.
doi: 10.1016/j.jfa.2011.09.002. |
[3] |
H. H. Bauschke and J. M. Borwein, On the convergence of von Neumann's alternating projection algorithm for two sets, Set-Valued Anal., 1 (1993), 185-212.
doi: 10.1007/BF01027691. |
[4] |
H. H. Bauschke, R. Burachik, P. L. Combettes, V. Elser, D. R. Luke and H. Wolkowicz, eds., Fixed-Point Algorithms for Inverse Problems in Science and Engineering, Springer-Verlag, New York, 2011.
doi: 10.1007/978-1-4419-9569-8. |
[5] |
H. H. Bauschke and P. L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, Springer, New York, 2011.
doi: 10.1007/978-1-4419-9467-7. |
[6] |
H. H. Bauschke and M. R. Edwards, A conjecture by De Pierro is true for translates of regular subspaces, J. Nonlinear Convex Anal., 6 (2005), 93-116. |
[7] |
H. H. Bauschke, X. Wang and C. J. S. Wylie, Fixed points of averages of resolvents: Geometry and algorithms, SIAM J. Optim., 22 (2012), 24-40.
doi: 10.1137/110823778. |
[8] |
H. Brézis, Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert, North-Holland/Elsevier, New York, 1973. |
[9] |
R. E. Bruck, Asymptotic convergence of nonlinear contraction semigroups in Hilbert space, J. Funct. Anal., 18 (1975), 15-26.
doi: 10.1016/0022-1236(75)90027-0. |
[10] |
C. L. Byrne, Applied Iterative Methods, A. K. Peters, Wellesley, MA, 2008. |
[11] |
A. Cegielski, Iterative Methods for Fixed Point Problems in Hilbert Spaces, Lecture Notes in Mathematics, 2057, Springer, Heidelberg, 2012. |
[12] |
Y. Censor, P. P. B. Eggermont and D. Gordon, Strong under-relaxation in Kaczmarz's method for inconsistent systems, Numer. Math., 41 (1983), 83-92.
doi: 10.1007/BF01396307. |
[13] |
P. L. Combettes, Inconsistent signal feasibility problems: Least-squares solutions in a product space, IEEE Trans. Signal Process., 42 (1994), 2955-2966.
doi: 10.1109/78.330356. |
[14] |
A. R. De Pierro, From parallel to sequential projection methods and vice versa in convex feasibility: Results and conjectures, in Inherently Parallel Algorithms for Feasibility and Optimization, Elsevier, New York, 2001, 187-201.
doi: 10.1016/S1570-579X(01)80012-4. |
[15] |
A. R. De Pierro and A. N. Iusem, A parallel projection method for finding a common point of a family of convex sets, Pesquisa Operacional, 5 (1985), 1-20. |
[16] |
L. G. Gubin, B. T. Polyak and E. V. Raik, The method of projections for finding the common point of convex sets, Comput. Math. Math. Phys., 7 (1967), 1-24.
doi: 10.1016/0041-5553(67)90113-9. |
[17] |
W. V. Petryshyn, Construction of fixed points of demicompact mappings in Hilbert space, J. Math. Anal. Appl., 14 (1966), 276-284.
doi: 10.1016/0022-247X(66)90027-8. |
[18] |
X. Wang and H. H. Bauschke, Compositions and averages of two resolvents: Relative geometry of fixed points sets and a partial answer to a question by C. Byrne, Nonlinear Anal., 74 (2011), 4550-4572.
doi: 10.1016/j.na.2011.04.024. |
[19] |
E. Zeidler, Nonlinear Functional Analysis and Its Applications II/B, Springer-Verlag, New York, 1990.
doi: 10.1007/978-1-4612-0985-0. |
show all references
References:
[1] |
H. Attouch, L. M. Briceño-Arias and P. L. Combettes, A parallel splitting method for coupled monotone inclusions, SIAM J. Control Optim., 48 (2010), 3246-3270.
doi: 10.1137/090754297. |
[2] |
J.-B. Baillon, P. L. Combettes and R. Cominetti, There is no variational characterization of the cycles in the method of periodic projections, J. Funct. Anal., 262 (2012), 400-408.
doi: 10.1016/j.jfa.2011.09.002. |
[3] |
H. H. Bauschke and J. M. Borwein, On the convergence of von Neumann's alternating projection algorithm for two sets, Set-Valued Anal., 1 (1993), 185-212.
doi: 10.1007/BF01027691. |
[4] |
H. H. Bauschke, R. Burachik, P. L. Combettes, V. Elser, D. R. Luke and H. Wolkowicz, eds., Fixed-Point Algorithms for Inverse Problems in Science and Engineering, Springer-Verlag, New York, 2011.
doi: 10.1007/978-1-4419-9569-8. |
[5] |
H. H. Bauschke and P. L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, Springer, New York, 2011.
doi: 10.1007/978-1-4419-9467-7. |
[6] |
H. H. Bauschke and M. R. Edwards, A conjecture by De Pierro is true for translates of regular subspaces, J. Nonlinear Convex Anal., 6 (2005), 93-116. |
[7] |
H. H. Bauschke, X. Wang and C. J. S. Wylie, Fixed points of averages of resolvents: Geometry and algorithms, SIAM J. Optim., 22 (2012), 24-40.
doi: 10.1137/110823778. |
[8] |
H. Brézis, Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert, North-Holland/Elsevier, New York, 1973. |
[9] |
R. E. Bruck, Asymptotic convergence of nonlinear contraction semigroups in Hilbert space, J. Funct. Anal., 18 (1975), 15-26.
doi: 10.1016/0022-1236(75)90027-0. |
[10] |
C. L. Byrne, Applied Iterative Methods, A. K. Peters, Wellesley, MA, 2008. |
[11] |
A. Cegielski, Iterative Methods for Fixed Point Problems in Hilbert Spaces, Lecture Notes in Mathematics, 2057, Springer, Heidelberg, 2012. |
[12] |
Y. Censor, P. P. B. Eggermont and D. Gordon, Strong under-relaxation in Kaczmarz's method for inconsistent systems, Numer. Math., 41 (1983), 83-92.
doi: 10.1007/BF01396307. |
[13] |
P. L. Combettes, Inconsistent signal feasibility problems: Least-squares solutions in a product space, IEEE Trans. Signal Process., 42 (1994), 2955-2966.
doi: 10.1109/78.330356. |
[14] |
A. R. De Pierro, From parallel to sequential projection methods and vice versa in convex feasibility: Results and conjectures, in Inherently Parallel Algorithms for Feasibility and Optimization, Elsevier, New York, 2001, 187-201.
doi: 10.1016/S1570-579X(01)80012-4. |
[15] |
A. R. De Pierro and A. N. Iusem, A parallel projection method for finding a common point of a family of convex sets, Pesquisa Operacional, 5 (1985), 1-20. |
[16] |
L. G. Gubin, B. T. Polyak and E. V. Raik, The method of projections for finding the common point of convex sets, Comput. Math. Math. Phys., 7 (1967), 1-24.
doi: 10.1016/0041-5553(67)90113-9. |
[17] |
W. V. Petryshyn, Construction of fixed points of demicompact mappings in Hilbert space, J. Math. Anal. Appl., 14 (1966), 276-284.
doi: 10.1016/0022-247X(66)90027-8. |
[18] |
X. Wang and H. H. Bauschke, Compositions and averages of two resolvents: Relative geometry of fixed points sets and a partial answer to a question by C. Byrne, Nonlinear Anal., 74 (2011), 4550-4572.
doi: 10.1016/j.na.2011.04.024. |
[19] |
E. Zeidler, Nonlinear Functional Analysis and Its Applications II/B, Springer-Verlag, New York, 1990.
doi: 10.1007/978-1-4612-0985-0. |
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