Jean-Bernard Baillon
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Jean-Bernard Baillon has a total of 3 co-authors. Here are the top co-authors by number of shared publications:
- Patrick L. Combettes
Department of Mathematics, North Carolina State University, Raleigh, USA
3 shared publications - Roberto Cominetti
Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Santiago 7941169, Chile
3 shared publications - Hedy Attouch
IMAG, Univ. Montpellier, CNRS, Montpellier, France
1 shared publication
Latest Publications
- 1 March 2018
- Published by Springer Nature in Vietnam Journal of Mathematics
- Vol. 46 (1) , 177-195
Weak Versus Strong Convergence of a Regularized Newton Dynamic for Maximal Monotone Operators
- 1 March 2018
- Published by Springer Nature in Vietnam Journal of Mathematics
- Vol. 46 (1) , 177-195
Weak Versus Strong Convergence of a Regularized Newton Dynamic for Maximal Monotone Operators
- Open Access
- 1 January 2014
- Published by American Institute of Mathematical Sciences (AIMS) in Journal of Dynamics and Games
- Vol. 1 (3) , 331-346
Asymptotic behavior ofcompositions of under-relaxed nonexpansive operators
In general there exists no relationship between the fixed point sets of the composition and of the average of a family of nonexpansive operators in Hilbert spaces. In this paper, we establish an asymptotic principle connecting the cycles generated by under-relaxed compositions of nonexpansive operators to the fixed points of the average of these operators. In the special case when the operators are projectors onto closed convex sets, we prove a conjecture by De Pierro which has so far been established only for projections onto affine subspaces.
- 1 January 2014
- Published by American Institute of Mathematical Sciences (AIMS) in Journal of Dynamics and Games
- Vol. 1 (3) , 331-346
Open AccessAsymptotic behavior ofcompositions of under-relaxed nonexpansive operators
In general there exists no relationship between the fixed point sets of the composition and of the average of a family of nonexpansive operators in Hilbert spaces. In this paper, we establish an asymptotic principle connecting the cycles generated by under-relaxed compositions of nonexpansive operators to the fixed points of the average of these operators. In the special case when the operators are projectors onto closed convex sets, we prove a conjecture by De Pierro which has so far been established only for projections onto affine subspaces.
- Open Access
Asymptotic behavior of compositions of under-relaxed nonexpansive operators
In general there exists no relationship between the fixed point sets of the composition and of the average of a family of nonexpansive operators in Hilbert spaces. In this paper, we establish an asymptotic principle connecting the cycles generated by under-relaxed compositions of nonexpansive operators to the fixed points of the average of these operators. In the special case when the operators are projectors onto closed convex sets, we prove a conjecture by De Pierro which has so far been established only for projections onto affine subspaces.
Open AccessAsymptotic behavior of compositions of under-relaxed nonexpansive operators
In general there exists no relationship between the fixed point sets of the composition and of the average of a family of nonexpansive operators in Hilbert spaces. In this paper, we establish an asymptotic principle connecting the cycles generated by under-relaxed compositions of nonexpansive operators to the fixed points of the average of these operators. In the special case when the operators are projectors onto closed convex sets, we prove a conjecture by De Pierro which has so far been established only for projections onto affine subspaces.
- Open Access
There is no variational characterization of the cycles in the method of periodic projections
The method of periodic projections consists in iterating projections onto $m$ closed convex subsets of a Hilbert space according to a periodic sweeping strategy. In the presence of $m\geq 3$ sets, a long-standing question going back to the 1960s is whether the limit cycles obtained by such a process can be characterized as the minimizers of a certain functional. In this paper we answer this question in the negative. Projection algorithms that minimize smooth convex functions over a product of convex sets are also discussed.Open AccessThere is no variational characterization of the cycles in the method of periodic projections
The method of periodic projections consists in iterating projections onto $m$ closed convex subsets of a Hilbert space according to a periodic sweeping strategy. In the presence of $m\geq 3$ sets, a long-standing question going back to the 1960s is whether the limit cycles obtained by such a process can be characterized as the minimizers of a certain functional. In this paper we answer this question in the negative. Projection algorithms that minimize smooth convex functions over a product of convex sets are also discussed.