Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local Convergence of the Heavy-ball Method and iPiano for Non-convex
  Optimization   A local convergence result for abstract descent methods is proved. The
sequence of iterates is attracted by a local (or global) minimum, stays in its
neighborhood and converges within this neighborhood. This result allows
algorithms to exploit local properties of the objective function. In
particular, the abstract theory in this paper applies to the inertial
forward--backward splitting method: iPiano---a generalization of the Heavy-ball
method. Moreover, it reveals an equivalence between iPiano and inertial
averaged/alternating proximal minimization and projection methods. Key for this
equivalence is the attraction to a local minimum within a neighborhood and the
fact that, for a prox-regular function, the gradient of the Moreau envelope is
locally Lipschitz continuous and expressible in terms of the proximal mapping.
In a numerical feasibility problem, the inertial alternating projection method
significantly outperforms its non-inertial variants.

27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
18
The categories of this paper are: econ