Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: General convergence analysis of stochastic first order methods for
  composite optimization   In this paper we consider stochastic composite convex optimization problems
with the objective function satisfying a stochastic bounded gradient condition,
with or without a quadratic functional growth property. These models include
the most well-known classes of objective functions analyzed in the literature:
non-smooth Lipschitz functions and composition of a (potentially) non-smooth
function and a smooth function, with or without strong convexity. Based on the
flexibility offered by our optimization model we consider several variants of
stochastic first order methods, such as the stochastic proximal gradient and
the stochastic proximal point algorithms. Usually, the convergence theory for
these methods has been derived for simple stochastic optimization models
satisfying restrictive assumptions, the rates are in general sublinear and hold
only for specific decreasing stepsizes. Hence, we analyze the convergence rates
of stochastic first order methods with constant or variable stepsize under
general assumptions covering a large class of objective functions. For constant
stepsize we show that these methods can achieve linear convergence rate up to a
constant proportional to the stepsize and under some strong stochastic bounded
gradient condition even pure linear convergence. Moreover, when a variable
stepsize is chosen we derive sublinear convergence rates for these stochastic
first order methods. Finally, the stochastic gradient mapping and the Moreau
smoothing mapping introduced in the present paper lead to simple and intuitive
proofs.

7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess