Finding Low-rank Solutions to Matrix Problems, Efficiently and Provably

@article{Park2016FindingLS,
  title={Finding Low-rank Solutions to Matrix Problems, Efficiently and Provably},
  author={Dohyung Park and Anastasios Kyrillidis and Constantine Caramanis and Sujay Sanghavi},
  journal={CoRR},
  year={2016},
  volume={abs/1606.03168}
}
A rank-r matrix X ∈ Rm×n can be written as a product UV >, where U ∈ Rm×r and V ∈ Rn×r. One could exploit this observation in optimization: e.g., consider the minimization of a convex function f(X) over rank-r matrices, where the scaffold of rank-r matrices is modeled via the factorization in U and V variables. Such heuristic has been widely used before for specific problem instances, where the solution sought is (approximately) low-rank. Though such parameterization reduces the number of… CONTINUE READING
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