Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of the Frank-Wolfe Method for Convex Composite Optimization
  involving a Logarithmically-Homogeneous Barrier   We present and analyze a new generalized Frank-Wolfe method for the composite
optimization problem $(P):{\min}_{x\in\mathbb{R}^n}\; f(\mathsf{A} x) + h(x)$,
where $f$ is a $\theta$-logarithmically-homogeneous self-concordant barrier,
$\mathsf{A}$ is a linear operator and the function $h$ has bounded domain but
is possibly non-smooth. We show that our generalized Frank-Wolfe method
requires $O((\delta_0 + \theta + R_h)\ln(\delta_0) + (\theta +
R_h)^2/\varepsilon)$ iterations to produce an $\varepsilon$-approximate
solution, where $\delta_0$ denotes the initial optimality gap and $R_h$ is the
variation of $h$ on its domain. This result establishes certain intrinsic
connections between $\theta$-logarithmically homogeneous barriers and the
Frank-Wolfe method. When specialized to the $D$-optimal design problem, we
essentially recover the complexity obtained by Khachiyan using the Frank-Wolfe
method with exact line-search. We also study the (Fenchel) dual problem of
$(P)$, and we show that our new method is equivalent to an adaptive-step-size
mirror descent method applied to the dual problem. This enables us to provide
iteration complexity bounds for the mirror descent method despite even though
the dual objective function is non-Lipschitz and has unbounded domain. In
addition, we present computational experiments that point to the potential
usefulness of our generalized Frank-Wolfe method on Poisson image de-blurring
problems with TV regularization, and on simulated PET problem instances.

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The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: stat