Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inertial Proximal Block Coordinate Method for a Class of Nonsmooth
  Sum-of-Ratios Optimization Problems   In this paper, we consider a class of nonsmooth sum-of-ratios fractional
optimization problems with block structure. This model class is ubiquitous and
encompasses several important nonsmooth optimization problems in the
literature. We first propose an inertial proximal block coordinate method for
solving this class of problems by exploiting the underlying structure. The
global convergence of our method is guaranteed under the
Kurdyka--{\L}ojasiewicz (KL) property and some mild assumptions. We then
identify the explicit exponents of the KL property for three important
structured fractional optimization problems. In particular, for the sparse
generalized eigenvalue problem with either cardinality regularization or
sparsity constraint, we show that the KL exponents are 1/2, and so, the
proposed method exhibits linear convergence rate. Finally, we illustrate our
theoretical results with both analytic and simulated numerical examples.

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The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys