Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sparse Generalized Eigenvalue Problem via Smooth Optimization   In this paper, we consider an $\ell_{0}$-norm penalized formulation of the
generalized eigenvalue problem (GEP), aimed at extracting the leading sparse
generalized eigenvector of a matrix pair. The formulation involves maximization
of a discontinuous nonconcave objective function over a nonconvex constraint
set, and is therefore computationally intractable. To tackle the problem, we
first approximate the $\ell_{0}$-norm by a continuous surrogate function. Then
an algorithm is developed via iteratively majorizing the surrogate function by
a quadratic separable function, which at each iteration reduces to a regular
generalized eigenvalue problem. A preconditioned steepest ascent algorithm for
finding the leading generalized eigenvector is provided. A systematic way based
on smoothing is proposed to deal with the "singularity issue" that arises when
a quadratic function is used to majorize the nondifferentiable surrogate
function. For sparse GEPs with special structure, algorithms that admit a
closed-form solution at every iteration are derived. Numerical experiments show
that the proposed algorithms match or outperform existing algorithms in terms
of computational complexity and support recovery.

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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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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: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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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: q-fin