Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Smooth minimization of nonsmooth functions with parallel coordinate
  descent methods   We study the performance of a family of randomized parallel coordinate
descent methods for minimizing the sum of a nonsmooth and separable convex
functions. The problem class includes as a special case L1-regularized L1
regression and the minimization of the exponential loss ("AdaBoost problem").
We assume the input data defining the loss function is contained in a sparse
$m\times n$ matrix $A$ with at most $\omega$ nonzeros in each row. Our methods
need $O(n \beta/\tau)$ iterations to find an approximate solution with high
probability, where $\tau$ is the number of processors and $\beta = 1 +
(\omega-1)(\tau-1)/(n-1)$ for the fastest variant. The notation hides
dependence on quantities such as the required accuracy and confidence levels
and the distance of the starting iterate from an optimal point. Since
$\beta/\tau$ is a decreasing function of $\tau$, the method needs fewer
iterations when more processors are used. Certain variants of our algorithms
perform on average only $O(\nnz(A)/n)$ arithmetic operations during a single
iteration per processor and, because $\beta$ decreases when $\omega$ does,
fewer iterations are needed for sparser problems.

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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int