Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parallel Successive Convex Approximation for Nonsmooth Nonconvex
  Optimization   Consider the problem of minimizing the sum of a smooth (possibly non-convex)
and a convex (possibly nonsmooth) function involving a large number of
variables. A popular approach to solve this problem is the block coordinate
descent (BCD) method whereby at each iteration only one variable block is
updated while the remaining variables are held fixed. With the recent advances
in the developments of the multi-core parallel processing technology, it is
desirable to parallelize the BCD method by allowing multiple blocks to be
updated simultaneously at each iteration of the algorithm. In this work, we
propose an inexact parallel BCD approach where at each iteration, a subset of
the variables is updated in parallel by minimizing convex approximations of the
original objective function. We investigate the convergence of this parallel
BCD method for both randomized and cyclic variable selection rules. We analyze
the asymptotic and non-asymptotic convergence behavior of the algorithm for
both convex and non-convex objective functions. The numerical experiments
suggest that for a special case of Lasso minimization problem, the cyclic block
selection rule can outperform the randomized rule.

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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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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: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn