title: Rank-Constrained Solutions to Linear Matrix Equations Using PowerFactorization.
abstract: Algorithms to construct/recover low-rank matrices satisfying a set of linear equality constraints have important applications in many signal processing contexts. Recently, theoretical guarantees for minimum-rank matrix recovery have been proven for nuclear norm minimization (NNM), which can be solved using standard convex optimization approaches. While nuclear norm minimization is effective, it can be computationally demanding. In this work, we explore the use of the PowerFactorization (PF) algorithm as a tool for rank-constrained matrix recovery. Empirical results indicate that incremented-rank PF is significantly more successful than NNM at recovering low-rank matrices, in addition to being faster.
authors.affiliation: The authors are with the Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801 USA ( haldar@uiuc.edu ;  dhernan2@illinois.edu ).
authors.forename: Justin P
authors.initials: JP
authors.lastname: Haldar
authors.forename: Diego
authors.initials: D
authors.lastname: Hernando