Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proximal ADMM for Nonconvex and Nonsmooth Optimization   By enabling the nodes or agents to solve small-sized subproblems to achieve
coordination, distributed algorithms are favored by many networked systems for
efficient and scalable computation. While for convex problems, substantial
distributed algorithms are available, the results for the more broad nonconvex
counterparts are extremely lacking. This paper develops a distributed algorithm
for a class of nonconvex and nonsmooth problems featured by i) a nonconvex
objective formed by both separate and composite objective components regarding
the decision components of interconnected agents, ii) local bounded convex
constraints, and iii) coupled linear constraints. This problem is directly
originated from smart buildings and is also broad in other domains. To provide
a distributed algorithm with convergence guarantee, we revise the powerful tool
of alternating direction method of multiplier (ADMM) and proposed a proximal
ADMM. Specifically, noting that the main difficulty to establish the
convergence for the nonconvex and nonsmooth optimization within the ADMM
framework is to assume the boundness of dual updates, we propose to update the
dual variables in a discounted manner. This leads to the establishment of a
so-called sufficiently decreasing and lower bounded Lyapunov function, which is
critical to establish the convergence. We prove that the method converges to
some approximate stationary points. We besides showcase the efficacy and
performance of the method by a numerical example and the concrete application
to multi-zone heating, ventilation, and air-conditioning (HVAC) control in
smart buildings.

8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph