Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A convergence framework for inexact nonconvex and nonsmooth algorithms
  and its applications to several iterations   In this paper, we consider the convergence of an abstract inexact nonconvex
and nonsmooth algorithm. We promise a pseudo sufficient descent condition and a
pseudo relative error condition, which are both related to an auxiliary
sequence, for the algorithm; and a continuity condition is assumed to hold. In
fact, a lot of classical inexact nonconvex and nonsmooth algorithms allow these
three conditions. Under a special kind of summable assumption on the auxiliary
sequence, we prove the sequence generated by the general algorithm converges to
a critical point of the objective function if being assumed Kurdyka-
Lojasiewicz property. The core of the proofs lies in building a new Lyapunov
function, whose successive difference provides a bound for the successive
difference of the points generated by the algorithm. And then, we apply our
findings to several classical nonconvex iterative algorithms and derive the
corresponding convergence results

15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th