Journal
MATHEMATICAL PROGRAMMING
Volume 129, Issue 2, Pages 163-195Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s10107-011-0472-0
Keywords
Proximal algorithm; Incremental method; Gradient method; Convex
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Funding
- AFOSR [FA9550-10-1-0412]
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We consider the minimization of a sum Sigma(m)(i=1) f(i)(x) consisting of a large number of convex component functions f(i). For this problem, incremental methods consisting of gradient or subgradient iterations applied to single components have proved very effective. We propose new incremental methods, consisting of proximal iterations applied to single components, as well as combinations of gradient, subgradient, and proximal iterations. We provide a convergence and rate of convergence analysis of a variety of such methods, including some that involve randomization in the selection of components. We also discuss applications in a few contexts, including signal processing and inference/machine learning.
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