Composite Self-Concordant Minimization

We propose a variable metric framework for minimizing the sum of a self-concordant function and a possibly non-smooth convex function endowed with a computable proximal operator. We theoretically establish the convergence of our framework without relying on the usual Lipschitz gradient assumption on the smooth part. An important highlight of our work is a new set of analytic step-size selection and correction procedures based on the structure of the problem. We describe concrete algorithmic instances of our framework for several interesting large-scale applications and demonstrate them numerically on both synthetic and real data.


Published in:
Journal of Machine Learning Research, 16, 371-416
Year:
2015
Publisher:
Massachusetts Institute of Technology Press
ISSN:
1532-4435
Keywords:
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 Record created 2013-08-13, last modified 2018-09-13

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