Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A New Insight on Augmented Lagrangian Method and Its Extensions   Motivated by the recent work [He-Yuan, Balanced Augmented Lagrangian Method
for Convex Programming, arXiv: 2108.08554v1, (2021)], a novel Augmented
Lagrangian Method (ALM) has been proposed for solving a family of convex
optimization problem subject to equality or inequality constraint. This new
method is then extended to solve the multi-block separable convex optimization
problem, and two related primal-dual hybrid gradient algorithms are also
discussed. Preliminary and some new convergence results are established with
the aid of variational analysis for both the saddle point of the problem and
the first-order optimality conditions of involved subproblems.

23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess