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Exploiting sparsity in polynomial optimization - lecture 2

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Auteurs : Magron, Victor (Auteur de la conférence)
CIRM (Editeur )

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Résumé : 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.

Mots-Clés : optimisation polynomiale; exploitation de la parcimonie; programmation semi-définie

Codes MSC :
65F50 - Sparse matrices
90C22 - Semidefinite programming
90C23 - Polynomial optimization

Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2888/Slides/SparsePOPJNCF23.pdf

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de Publication : 20/03/2023
    Date de Captation : 06/03/2023
    Sous Collection : Research School
    Catégorie arXiv : Optimization and Control
    Domaine(s) : Théorie du Contrôle & Optimisation
    Format : MP4 (.mp4) - HD
    Durée : 01:29:20
    Audience : Chercheurs ; Etudiants Science Cycle 2 ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2023-03-07_Magron.mp4

Informations sur la Rencontre

Nom de la Rencontre : Francophone Computer Algebra Days / JNCF - Journées nationales de calcul formel
Organisateurs de la Rencontre : Berthomieu, Jérémy ; Boito, Paola ; Guerrini, Eleonora ; Ollivier, François ; Spaenlehauer, Pierre-Jean
Dates : 06/03/2023 - 10/03/2023
Année de la rencontre : 2023
URL de la Rencontre : https://conferences.cirm-math.fr/2888.html

Données de citation

DOI : 10.24350/CIRM.V.20013803
Citer cette vidéo: Magron, Victor (2023). Exploiting sparsity in polynomial optimization - lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20013803
URI : http://dx.doi.org/10.24350/CIRM.V.20013803

Voir Aussi

Bibliographie

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