### Olivier Fercoq (University of Edinburgh)

#### Smooth minimization of nonsmooth functions by parallel coordinate descent

*Wednesday 27 February 2013 at 15.30, JCMB 6206*

##### Abstract

In this talk, we first show that coordinate descent methods can be efficiently
applied to the optimization of nonsmooth convex functions with explicit
max-structure. We derive a quadratic separable overapproximation of the
smoothed function obtained by Nesterov's smoothing and from it we derive the
iteration complexity of the Parallel Coordinate Descent Method applied to this
class of functions.

In a second part, we compare the Parallel Coordinate Descent Method with the
Monte Carlo approach, where we launch several times the serial randomized
coordinate descent method in order to reduce the variance of the random
process describing the value of the function. Using the theoretical iteration
complexity, we show that, depending on the problem at stake, both approaches
may be competitive, or that a nested parallelism may be better.

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