Work

Scalable Semidefinite Programming

Year: 2021

Type: article

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 \sf MaxCut, abstract phase retrieval, and quadratic assignment. Running on a laptop equivalent, the algorithm can handle SDP instances where the matrix variable has over $10^{14}$ entries.

Source: SIAM Journal on Mathematics of Data Science

DOI: 10.1137/19m1305045

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

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Science Foundation, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, Defense Advanced Research Projects Agency, Office of Naval Research

Awards: G1658625161, G1804926627, CAREER: Modern nonconvex optimization for machine learning: foundations of geometric and scalable techniques, G4254929486, G4296480827, G4432654340, Practical algorithms with rigorous guarantees for large-scale semidefinite programming

OpenAlex ID: W2992793632

FWCI: 11.34

Cites: 50

Cited by: 87

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