Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: One dimensional fractional order $TGV$: Gamma-convergence and bilevel
  training scheme   New fractional $r$-order seminorms, $TGV^r$, $r\in \mathbb R$, $r\geq 1$, are
proposed in the one-dimensional (1D) setting, as a generalization of the
integer order $TGV^k$-seminorms, $k\in\mathbb{N}$. The fractional $r$-order
$TGV^r$-seminorms are shown to be intermediate between the integer order
$TGV^k$-seminorms. A bilevel training scheme is proposed, where under a box
constraint a simultaneous optimization with respect to parameters and order of
derivation is performed. Existence of solutions to the bilevel training scheme
is proved by $\Gamma$-convergence. Finally, the numerical landscape of the cost
function associated to the bilevel training scheme is discussed for two
numerical examples.

10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci