Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Inexact Cyclic Block Proximal Gradient Method and Properties of
  Inexact Proximal Maps   This paper expands the Cyclic Block Proximal Gradient method for block
separable composite minimization by allowing for inexactly computed gradients
and proximal maps. The resultant algorithm, the Inexact Cyclic Block Proximal
Gradient (I-CBPG) method, shares the same convergence rate as its exactly
computed analogue provided the allowable errors decrease sufficiently quickly
or are pre-selected to be sufficiently small. We provide numerical experiments
that showcase the practical computational advantage of I-CBPG for certain fixed
tolerances of approximation error and for a dynamically decreasing error
tolerance regime in particular. We establish a tight relationship between
inexact proximal map evaluations and $\delta$-subgradients in our
$\delta$-Second Prox Theorem. This theorem forms the foundation of our
convergence analysis and enables us to show that inexact gradient computations
and other notions of inexact proximal map computation can be subsumed within a
single unifying framework.

22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat