Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence of a first-order consensus-based global optimization
  algorithm   Global optimization of a non-convex objective function often appears in
large-scale machine-learning and artificial intelligence applications.
Recently, consensus-based optimization (in short CBO) methods have been
introduced as one of the gradient-free optimization methods. In this paper, we
provide a convergence analysis for the first-order CBO method in
\cite{C-J-L-Z}. Prior to the current work, the convergence study was carried
out for CBO methods on corresponding mean-field limit, a Fokker-Planck
equation, which does not imply the convergence of the CBO method {\it per se}.
Based on the consensus estimate directly on the first-order CBO model, we
provide a convergence analysis of the first-order CBO method \cite{C-J-L-Z}
without resorting to the corresponding mean-field model. Our convergence
analysis consists of two steps. In the first step, we show that the CBO model
exhibits a global consensus time asymptotically for any initial data, and in
the second step, we provide a sufficient condition on system parameters--which
is dimension independent-- and initial data which guarantee that the converged
consensus state lies in a small neighborhood of the global minimum almost
surely.

7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat