On the Convergence of Projected-Gradient Methods with Low-Rank Projections for Smooth Convex Minimization over Trace-Norm Balls and Related Problems

Smooth convex minimization over the unit trace-norm ball is an important optimization problem in machine learning, signal processing, statistics and other fields, that underlies many tasks in which one wishes to recover a low-rank matrix given certain measurements. While first-order methods for convex optimization enjoy optimal convergence rates, they require in worst-case to compute a full-rank SVD on each iteration, in order to compute the projection onto the trace-norm ball... (read more)

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