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Exploiting sparsity in polynomial optimization - lecture 1
Multi angle
Authors : Magron, Victor (Author of the conference)
CIRM (Publisher )
65F50 - Sparse matrices
90C22 - Semidefinite programming
90C23 - Polynomial optimization
Additional resources :
https://www.cirm-math.fr/RepOrga/2888/Slides/SparsePOPJNCF23.pdf
CIRM (Publisher )
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Abstract :
Polynomial optimization methods often encompass many major scalability issues on the practical side. Fortunately, for many real-world problems, we can look at them in the eyes and exploit the inherent data structure arising from the input cost and constraints. The first part of my lecture will focus on the notion of 'correlative sparsity', occurring when there are few correlations between the variables of the input problem. The second part will present a complementary framework, where we show how to exploit a distinct notion of sparsity, called 'term sparsity', occurring when there are a small number of terms involved in the input problem by comparison with the fully dense case. At last but not least, I will present a very recently developed type of sparsity that we call 'ideal-sparsity', which exploits the presence of equality constraints. Several illustrations will be provided on important applications arising from various fields, including computer arithmetic, robustness of deep networks, quantum entanglement, optimal power-flow, and matrix factorization ranks.
Keywords : optimisation polynomiale; exploitation de la parcimonie; programmation semi-définie
MSC Codes : Keywords : optimisation polynomiale; exploitation de la parcimonie; programmation semi-définie
65F50 - Sparse matrices
90C22 - Semidefinite programming
90C23 - Polynomial optimization
Additional resources :
https://www.cirm-math.fr/RepOrga/2888/Slides/SparsePOPJNCF23.pdf
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Information on the Video
Film maker : Petit, JeanLanguage : English Available date : 20/03/2023 Conference Date : 06/03/2023 Subseries : Research School arXiv category : Optimization and Control Mathematical Area(s) : Control Theory & Optimization Format : MP4 (.mp4) - HD Video Time : 01:29:05 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-03-06_Magron.mp4 
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Information on the Event
Event Title : Francophone Computer Algebra Days / JNCF - Journées nationales de calcul formelEvent Organizers : Berthomieu, Jérémy ; Boito, Paola ; Guerrini, Eleonora ; Ollivier, François ; Spaenlehauer, Pierre-Jean Dates : 06/03/2023 - 10/03/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2888.html
Citation Data
DOI : 10.24350/CIRM.V.20013503Cite this video as: Magron, Victor (2023). Exploiting sparsity in polynomial optimization - lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20013503 URI : http://dx.doi.org/10.24350/CIRM.V.20013503 |
See Also
- [Multi angle] Using structured variants in lattice-based cryptography - lecture 2 / Author of the conference Roux-Langlois, Adeline.
- [Multi angle] Exploiting sparsity in polynomial optimization - lecture 2 / Author of the conference Magron, Victor.
- [Multi angle] Using structured variants in lattice-based cryptography - lecture 1 / Author of the conference Roux-Langlois, Adeline.
Bibliography
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