Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Iterative Reweighted Minimization Methods for $l_p$ Regularized
  Unconstrained Nonlinear Programming   In this paper we study general $l_p$ regularized unconstrained minimization
problems. In particular, we derive lower bounds for nonzero entries of first-
and second-order stationary points, and hence also of local minimizers of the
$l_p$ minimization problems. We extend some existing iterative reweighted $l_1$
(IRL1) and $l_2$ (IRL2) minimization methods to solve these problems and
proposed new variants for them in which each subproblem has a closed form
solution. Also, we provide a unified convergence analysis for these methods. In
addition, we propose a novel Lipschitz continuous $\epsilon$-approximation to
$\|x\|^p_p$. Using this result, we develop new IRL1 methods for the $l_p$
minimization problems and showed that any accumulation point of the sequence
generated by these methods is a first-order stationary point, provided that the
approximation parameter $\epsilon$ is below a computable threshold value. This
is a remarkable result since all existing iterative reweighted minimization
methods require that $\epsilon$ be dynamically updated and approach zero. Our
computational results demonstrate that the new IRL1 method is generally more
stable than the existing IRL1 methods [21,18] in terms of objective function
value and CPU time.

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The categories of this paper are: q-bio
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The categories of this paper are: physics
26
The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org