Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Theoretical and numerical comparison of first-order algorithms for
  cocoercive equations and smooth convex optimization   This paper provides a theoretical and numerical comparison of classical
first-order splitting methods for solving smooth convex optimization problems
and cocoercive equations. In a theoretical point of view, we compare
convergence rates of gradient descent, forward-backward, Peaceman-Rachford, and
Douglas-Rachford algorithms for minimizing the sum of two smooth convex
functions when one of them is strongly convex. A similar comparison is given in
the more general cocoercive setting under the presence of strong monotonicity
and we observe that the convergence rates in optimization are strictly better
than the corresponding rates for cocoercive equations for some algorithms. We
obtain improved rates with respect to the literature in several instances
exploiting the structure of our problems. Moreover, we indicate which algorithm
is the most efficient depending on strong convexity and cocoercive parameters.
In a numerical point of view, we verify our theoretical results by implementing
and comparing previous algorithms in well-established signal and image inverse
problems involving sparsity. We replace the widely used $\ell_1$ norm by the
Huber loss and we observe that fully proximal-based strategies have numerical
and theoretical advantages with respect to methods using gradient steps.

36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio