Heinz H. Bauschke
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
Research Subjects
Heinz H. Bauschke has a total of 128 co-authors. Here are the top co-authors by number of shared publications:
- Xianfu Wang
Department of Mathematics, I.K. Barber Faculty of Science, University of British Columbia Okanagan, Kelowna, Canada
96 shared publications - Patrick L. Combettes
Department of Mathematics, North Carolina State University, Raleigh, USA
46 shared publications - Walaa M. Moursi
University of Waterloo
33 shared publications Xianfu Wang
Mathematics, University of British Columbia, Kelowna, Canada
18 shared publications- Jonathan Michael Borwein
Dalhousie University
14 shared publications - Liangjin Yao
University of British Columbia
14 shared publications
Latest Publications
- 21 October 2026
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Optimization
- Vol. 36 (4) , 2296-2312
Extending Meshulam’s Result on the Boundedness of Orbits of Relaxed Projections onto Affine Subspaces from Finite to Infinite-Dimensional Hilbert Spaces
In 1996, Meshulam proved that any sequence generated in Euclidean space by randomly projecting onto affine subspaces drawn from a finite collection stays bounded even if the intersection of the subspaces is empty. His proof, which works even for relaxed projections, relies on an ingenious induction on the dimension of the Euclidean space. In this paper, we extend Meshulam’s result to the general Hilbert space setting by an induction proof on the number of affine subspaces in the given collection. We require that the corresponding parallel linear subspaces are innately regular—this assumption always holds in Euclidean space. We also discuss the sharpness of our result and make a connection to randomized block Kaczmarz methods.
- 21 October 2026
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Optimization
- Vol. 36 (4) , 2296-2312
Extending Meshulam’s Result on the Boundedness of Orbits of Relaxed Projections onto Affine Subspaces from Finite to Infinite-Dimensional Hilbert Spaces
In 1996, Meshulam proved that any sequence generated in Euclidean space by randomly projecting onto affine subspaces drawn from a finite collection stays bounded even if the intersection of the subspaces is empty. His proof, which works even for relaxed projections, relies on an ingenious induction on the dimension of the Euclidean space. In this paper, we extend Meshulam’s result to the general Hilbert space setting by an induction proof on the number of affine subspaces in the given collection. We require that the corresponding parallel linear subspaces are innately regular—this assumption always holds in Euclidean space. We also discuss the sharpness of our result and make a connection to randomized block Kaczmarz methods.
- 30 September 2026
- Published by Springer Nature in Numerical Algorithms
- p. 1-37
Boţ–Nguyen acceleration, weighted mean ergodic iteration, and the beta-binomial distribution
- 30 September 2026
- Published by Springer Nature in Numerical Algorithms
- p. 1-37
Boţ–Nguyen acceleration, weighted mean ergodic iteration, and the beta-binomial distribution
- 25 September 2026
- Published by Elsevier in Journal of Approximation Theory
- Vol. 321-322
The Güntürk–Thao theorem revisited: Polyhedral cones and limiting examples
- 25 September 2026
- Published by Elsevier in Journal of Approximation Theory
- Vol. 321-322
The Güntürk–Thao theorem revisited: Polyhedral cones and limiting examples
- 2 September 2026
- Published by Springer Nature
- p. 609-621
Improving Computational Efficiency in Robust SVM Under Label Uncertainty
- 2 September 2026
- Published by Springer Nature
- p. 609-621
Improving Computational Efficiency in Robust SVM Under Label Uncertainty
- 12 August 2026
- Published by Springer Nature in Journal of Optimization Theory and Applications
- Vol. 210 (3) , 46
Fejér and Fejér* Monotonicity: Differences, Similarities, and the Role of the Relative Interior
- 12 August 2026
- Published by Springer Nature in Journal of Optimization Theory and Applications
- Vol. 210 (3) , 46
Fejér and Fejér* Monotonicity: Differences, Similarities, and the Role of the Relative Interior
- 7 July 2026
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Optimization
- Vol. 36 (3) , 1297-1325
Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting
In this work, we develop a convergence framework for iterative algorithms whose updates can be described by a one-parameter family of nonexpansive operators. Within the framework, each step involving one of the main algorithmic operators is followed by a second step which “relocates” fixed points of the current operator to the next. As a consequence, our analysis does not require the family of nonexpansive operators to have a common fixed point, as frequently assumed in the literature. Our analysis uses a parametric extension of the demiclosedness principle for nonexpansive operators. As an application of our convergence results, we develop a version of the graph-based extension of the Douglas–Rachford algorithm for finding a zero of the sum of [Formula: see text] maximally monotone operators, which does not require the resolvent parameter to be constant across iterations.
- 7 July 2026
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Optimization
- Vol. 36 (3) , 1297-1325
Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting
In this work, we develop a convergence framework for iterative algorithms whose updates can be described by a one-parameter family of nonexpansive operators. Within the framework, each step involving one of the main algorithmic operators is followed by a second step which “relocates” fixed points of the current operator to the next. As a consequence, our analysis does not require the family of nonexpansive operators to have a common fixed point, as frequently assumed in the literature. Our analysis uses a parametric extension of the demiclosedness principle for nonexpansive operators. As an application of our convergence results, we develop a version of the graph-based extension of the Douglas–Rachford algorithm for finding a zero of the sum of [Formula: see text] maximally monotone operators, which does not require the resolvent parameter to be constant across iterations.
- 16 April 2026
- Published by Springer Nature in Journal of Optimization Theory and Applications
- Vol. 209 (2) , 41
Baillon-Bruck-Reich Revisited: Divergent-Series Parameters and Strong Convergence in the Linear Case
- 16 April 2026
- Published by Springer Nature in Journal of Optimization Theory and Applications
- Vol. 209 (2) , 41
Baillon-Bruck-Reich Revisited: Divergent-Series Parameters and Strong Convergence in the Linear Case
- Open Access
Extending Meshulam's result on the boundedness of orbits of relaxed projections onto affine subspaces from finite to infinite-dimensional Hilbert spaces
In 1996, Meshulam proved that any sequence generated in Euclidean space by randomly projecting onto affine subspaces drawn from a finite collection stays bounded even if the intersection of the subspaces is empty. His proof, which works even for relaxed projections, relies on an ingenious induction on the dimension of the Euclidean space. In this paper, we extend Meshulam's result to the general Hilbert space setting by an induction proof of the number of affine subspaces in the given collection. We require that the corresponding parallel linear subspaces are innately regular -- this assumption always holds in Euclidean space. We also discuss the sharpness of our result and make a connection to randomized block Kaczmarz methods.
Open AccessExtending Meshulam's result on the boundedness of orbits of relaxed projections onto affine subspaces from finite to infinite-dimensional Hilbert spaces
In 1996, Meshulam proved that any sequence generated in Euclidean space by randomly projecting onto affine subspaces drawn from a finite collection stays bounded even if the intersection of the subspaces is empty. His proof, which works even for relaxed projections, relies on an ingenious induction on the dimension of the Euclidean space. In this paper, we extend Meshulam's result to the general Hilbert space setting by an induction proof of the number of affine subspaces in the given collection. We require that the corresponding parallel linear subspaces are innately regular -- this assumption always holds in Euclidean space. We also discuss the sharpness of our result and make a connection to randomized block Kaczmarz methods.
- Open Access
The Güntürk-Thao theorem revisited: polyhedral cones and limiting examples
In 2023, Güntürk and Thao proved that the sequence $(x^{(n)})_{n\in\mathbb{N}}$ generated by random (relaxed) projections drawn from a finite collection of innately regular closed subspaces in a real Hilbert space satisfies $\sum_{n\in\mathbb{N}} \|x^{(n)}-x^{(n+1)}\|^γ<+\infty$ for all $γ>0$. We extend their result to a finite collection of polyhedral cones. Moreover, we construct examples showing the tightness of our extension: indeed, the result fails for a line and a convex set in $\mathbb{R}^2$, and for a plane and a non-polyhedral cone in $\mathbb{R}^3$.Open AccessThe Güntürk-Thao theorem revisited: polyhedral cones and limiting examples
In 2023, Güntürk and Thao proved that the sequence $(x^{(n)})_{n\in\mathbb{N}}$ generated by random (relaxed) projections drawn from a finite collection of innately regular closed subspaces in a real Hilbert space satisfies $\sum_{n\in\mathbb{N}} \|x^{(n)}-x^{(n+1)}\|^γ<+\infty$ for all $γ>0$. We extend their result to a finite collection of polyhedral cones. Moreover, we construct examples showing the tightness of our extension: indeed, the result fails for a line and a convex set in $\mathbb{R}^2$, and for a plane and a non-polyhedral cone in $\mathbb{R}^3$.