Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The multiproximal linearization method for convex composite problems   Composite minimization involves a collection of smooth functions which are
aggregated in a nonsmooth manner. In the convex setting, we design an algorithm
by linearizing each smooth component in accordance with its main curvature. The
resulting method, called the Multiprox method, consists in solving successively
simple problems (e.g. constrained quadratic problems) which can also feature
some proximal operators. To study the complexity and the convergence of this
method we are led to study quantitative qualification conditions to understand
the impact of multipliers on the complexity bounds. We obtain explicit
complexity results of the form $O(\frac{1}{k})$ involving new types of constant
terms. A distinctive feature of our approach is to be able to cope with oracles
involving moving constraints. Our method is flexible enough to include the
moving balls method, the proximal Gauss-Newton's method, or the
forward-backward splitting, for which we recover known complexity results or
establish new ones. We show through several numerical experiments how the use
of multiple proximal terms can be decisive for problems with complex
geometries.

16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an