Matrix and Operator Scaling

Graduate Seminar on Discrete Optimization (S4C1), Winter 2024/25

Course information

Slides from the planning meeting

Schedule

Regular talks normally run 14:15-15:45, and practice talks on 16:00-17:30 on Friday. The seminars will take place at the Hertz chair seminar room on the 1st floor of Poppelsdorfer Allee 24. Please ring the doorbell at the building entrance.

Nr. Practice talk Presentation Name Topic Mentoring
1 15.11. 22.11. Yelyzaveta Shvoieva Kalantari, B., & Khachiyan, L. (1996).
On the complexity of nonnegative-matrix scaling.
Haoyuan Ma
2 15.11. 29.11. Svenja Matthes Rote, G., & Zachariasen, M. (2007).
Matrix scaling by network flow
Haoyuan Ma
3 29.11. 13.12. Mahmut Can Yavuz Chakrabarty, D., & Khanna, S. (2021).
Better and simpler error analysis of the Sinkhorn-Knopp algorithm for matrix scaling
Haoyuan Ma
4 13.12. 20.12. Henri Saal Linial, N., Samorodnitsky, A., & Wigderson, A. (2000).
A Deterministic Strongly Polynomial Algorithm for Matrix Scaling and Approximate Permanents
Haoyuan Ma
5 20.12. 10.01. Adrian Glubrecht Garg, A., Gurvits, L., Oliveira, R., & Wigderson, A. (2020).
Operator scaling: theory and applications
Part 1
Matthias Kaul
6 TBC 17.01. David Čadež Garg, A., Gurvits, L., Oliveira, R., & Wigderson, A. (2020).
Operator scaling: theory and applications
Part 2
Matthias Kaul
7 10.01 24.01. Louis Carlin Garg, A., Gurvits, L., Oliveira, R., & Wigderson, A. (2018).
Algorithmic and optimization aspects of Brascamp-Lieb inequalities, via operator scaling
Matthias Kaul

List of papers

Chakrabarty, D., & Khanna, S. (2021). Better and simpler error analysis of the Sinkhorn-Knopp algorithm for matrix scaling.
Mathematical Programming, 188(1), 395–407.
Link
Kalantari, B., & Khachiyan, L. (1996). On the complexity of nonnegative-matrix scaling.
Linear Algebra and its applications, 240, 87–103.
Link
Rote, G., & Zachariasen, M. (2007). Matrix scaling by network flow.
Proceedings of the eighteenth annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 848–854
Link
Linial, N., Samorodnitsky, A., & Wigderson, A. (2000).
A Deterministic Strongly Polynomial Algorithm for Matrix Scaling and Approximate Permanents. Combinatorica, 20(4), 545–568.
Link
Idel, M. (2016). A review of matrix scaling and Sinkhorn's normal form for matrices and positive maps.
arXiv:1609.06349, Link
Garg, A., Gurvits, L., Oliveira, R., & Wigderson, A. (2020). Operator scaling: theory and applications.
Foundations of Computational Mathematics, 20(2), 223–290. Link
Garg, A., Gurvits, L., Oliveira, R., & Wigderson, A. (2018). Algorithmic and optimization aspects of Brascamp–Lieb inequalities, via operator scaling.
Geom. Funct. Anal, 28, 100–145. Link

Further resources

Avi Wigderson (2017). Operator Scaling: Theory, Applications and Connections
lecture notes.
Link