Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: NESTT: A Nonconvex Primal-Dual Splitting Method for Distributed and
  Stochastic Optimization   We study a stochastic and distributed algorithm for nonconvex problems whose
objective consists of a sum of $N$ nonconvex $L_i/N$-smooth functions, plus a
nonsmooth regularizer. The proposed NonconvEx primal-dual SpliTTing (NESTT)
algorithm splits the problem into $N$ subproblems, and utilizes an augmented
Lagrangian based primal-dual scheme to solve it in a distributed and stochastic
manner. With a special non-uniform sampling, a version of NESTT achieves
$\epsilon$-stationary solution using
$\mathcal{O}((\sum_{i=1}^N\sqrt{L_i/N})^2/\epsilon)$ gradient evaluations,
which can be up to $\mathcal{O}(N)$ times better than the (proximal) gradient
descent methods. It also achieves Q-linear convergence rate for nonconvex
$\ell_1$ penalized quadratic problems with polyhedral constraints. Further, we
reveal a fundamental connection between primal-dual based methods and a few
primal only methods such as IAG/SAG/SAGA.

23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph