14,821 research outputs found
Matrix Recipes for Hard Thresholding Methods
In this paper, we present and analyze a new set of low-rank recovery
algorithms for linear inverse problems within the class of hard thresholding
methods. We provide strategies on how to set up these algorithms via basic
ingredients for different configurations to achieve complexity vs. accuracy
tradeoffs. Moreover, we study acceleration schemes via memory-based techniques
and randomized, -approximate matrix projections to decrease the
computational costs in the recovery process. For most of the configurations, we
present theoretical analysis that guarantees convergence under mild problem
conditions. Simulation results demonstrate notable performance improvements as
compared to state-of-the-art algorithms both in terms of reconstruction
accuracy and computational complexity.Comment: 26 page
Smooth Primal-Dual Coordinate Descent Algorithms for Nonsmooth Convex Optimization
We propose a new randomized coordinate descent method for a convex
optimization template with broad applications. Our analysis relies on a novel
combination of four ideas applied to the primal-dual gap function: smoothing,
acceleration, homotopy, and coordinate descent with non-uniform sampling. As a
result, our method features the first convergence rate guarantees among the
coordinate descent methods, that are the best-known under a variety of common
structure assumptions on the template. We provide numerical evidence to support
the theoretical results with a comparison to state-of-the-art algorithms.Comment: NIPS 201
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