Quartic First-Order Methods for Low-Rank Minimization

We study a general nonconvex formulation for low-rank minimization problems. We use recent results on non-Euclidean first-order methods to provide efficient and scalable algorithms. Our approach uses the geometry induced by the Bregman divergence of well-chosen kernel functions; for unconstrained pr...

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Bibliographic Details
Published in:	Journal of optimization theory and applications Vol. 189; no. 2; pp. 341 - 363
Main Authors:	Dragomir, Radu-Alexandru, d’Aspremont, Alexandre, Bolte, Jérôme
Format:	Journal Article
Language:	English
Published:	New York Springer US 01-05-2021 Springer Nature B.V
Subjects:	Algorithms Applications of Mathematics Calculus of Variations and Optimal Control; Optimization Divergence Engineering Euclidean geometry Kernel functions Mathematical analysis Mathematics Mathematics and Statistics Matrix methods Operations Research/Decision Theory Optimization Theory of Computation Burer–Monteiro Euclidean distance matrix completion Low-rank minimization 90C06 Matrix factorization 90C26 Bregman first-order methods
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