### Ion Necoara (University of Bucharest)

#### Random coordinate descent methods for large scale problems

*Wednesday 25 June 2014 at 13.30, JCMB 6206*

##### Abstract

In this talk we present randomized block coordinate descent methods for
minimizing convex optimization problems with linearly coupled constraints over
networks and show that they obtain in expectation an ε-accurate
solution in at most O(N/ε) iterations, where N is the number of nodes
in the network. However, the computational complexity per iteration of these
methods is much simpler than the one of a method based on full gradient
information and each iteration can be computed in a distributed way. We focus
on how to choose the probabilities to make these randomized algorithms to
converge as fast as possible and we arrive at solving sparse SDPs. Analysis
for rate of convergence in probability is also provided. For strongly convex
functions we show that these distributed algorithms converge linearly. We also
discuss the extension of these algorithms to composite convex optimization and
nonconvex optimization and show that similar results hold. Finally, we provide
some numerical applications and comparisons with alternative strategies from
the literature.

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