Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distributed Continuous-Time and Discrete-Time Optimization With
  Nonuniform Unbounded Convex Constraint Sets and Nonuniform Stepsizes   This paper is devoted to distributed continuous-time and discrete-time
optimization problems with nonuniform convex constraint sets and nonuniform
stepsizes for general differentiable convex objective functions. The
communication graphs are not required to be strongly connected at any time, the
gradients of the local objective functions are not required to be bounded when
their independent variables tend to infinity, and the constraint sets are not
required to be bounded. For continuous-time multi-agent systems, a distributed
continuous algorithm is first introduced where the stepsizes and the convex
constraint sets are both nonuniform. It is shown that all agents reach a
consensus while minimizing the team objective function even when the constraint
sets are unbounded. After that, the obtained results are extended to
discrete-time multi-agent systems and then the case where each agent remains in
a corresponding convex constraint set is studied. To ensure all agents to
remain in a bounded region, a switching mechanism is introduced in the
algorithms. It is shown that the distributed optimization problems can be
solved, even though the discretization of the algorithms might deviate the
convergence of the agents from the minimum of the objective functions. Finally,
numerical examples are included to show the obtained theoretical results.

10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg