Scalable Semidefinite Programming

Alp Yurtsever; Joel A. Tropp; Olivier Fercoq; Madeleine Udell; Volkan Cevher

doi:10.1137/19M1305045

Scalable Semidefinite Programming

Alp Yurtsever
, Joel A. Tropp
, Olivier Fercoq
, Madeleine Udell
, Volkan Cevher

ENAC-IIC-GEL
Massachusetts Institute of Technology
California Institute of Technology Division of Engineering and Applied Science
Cornell University College of Engineering

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

97 Citations (Scopus)

Résumé

Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP problems by economizing on the storage and arithmetic costs. Numerical evidence shows that the method is effective for a range of applications, including relaxations of MaxCut, abstract phase retrieval, and quadratic assignment. Running on a laptop equivalent, the algorithm can handle SDP instances where the matrix variable has over 10¹⁴ entries.

langue originale	Anglais
Pages (de - à)	171-200
Nombre de pages	30
journal	SIAM Journal on Mathematics of Data Science
Volume	3
Numéro de publication	1
Les DOIs	https://doi.org/10.1137/19M1305045
état	Publié - 1 janv. 2020

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title = "Scalable Semidefinite Programming",

abstract = "Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP problems by economizing on the storage and arithmetic costs. Numerical evidence shows that the method is effective for a range of applications, including relaxations of MaxCut, abstract phase retrieval, and quadratic assignment. Running on a laptop equivalent, the algorithm can handle SDP instances where the matrix variable has over 1014 entries.",

keywords = "augmented Lagrangian, conditional gradient method, convex optimization, dimension reduction, first-order method, randomized linear algebra, semidefinite programming, sketching",

author = "Alp Yurtsever and Tropp, \{Joel A.\} and Olivier Fercoq and Madeleine Udell and Volkan Cevher",

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AU - Fercoq, Olivier

AU - Udell, Madeleine

AU - Cevher, Volkan

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KW - augmented Lagrangian

KW - conditional gradient method

KW - convex optimization

KW - dimension reduction

KW - first-order method

KW - randomized linear algebra

KW - semidefinite programming

KW - sketching

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Scalable Semidefinite Programming

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