Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: First-order methods for constrained convex programming based on
  linearized augmented Lagrangian function   First-order methods have been popularly used for solving large-scale
problems. However, many existing works only consider unconstrained problems or
those with simple constraint. In this paper, we develop two first-order methods
for constrained convex programs, for which the constraint set is represented by
affine equations and smooth nonlinear inequalities. Both methods are based on
the classic augmented Lagrangian function. They update the multipliers in the
same way as the augmented Lagrangian method (ALM) but employ different primal
variable updates. The first method, at each iteration, performs a single
proximal gradient step to the primal variable, and the second method is a block
update version of the first one.
  For the first method, we establish its global iterate convergence as well as
global sublinear and local linear convergence, and for the second method, we
show a global sublinear convergence result in expectation. Numerical
experiments are carried out on the basis pursuit denoising and a convex
quadratically constrained quadratic program to show the empirical performance
of the proposed methods. Their numerical behaviors closely match the
established theoretical results.

19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin