Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local and Global Convergence of a General Inertial Proximal Splitting
  Scheme   This paper is concerned with convex composite minimization problems in a
Hilbert space. In these problems, the objective is the sum of two closed,
proper, and convex functions where one is smooth and the other admits a
computationally inexpensive proximal operator. We analyze a general family of
inertial proximal splitting algorithms (GIPSA) for solving such problems. We
establish finiteness of the sum of squared increments of the iterates and
optimality of the accumulation points. Weak convergence of the entire sequence
then follows if the minimum is attained. Our analysis unifies and extends
several previous results.
  We then focus on $\ell_1$-regularized optimization, which is the ubiquitous
special case where the nonsmooth term is the $\ell_1$-norm. For certain
parameter choices, GIPSA is amenable to a local analysis for this problem. For
these choices we show that GIPSA achieves finite "active manifold
identification", i.e. convergence in a finite number of iterations to the
optimal support and sign, after which GIPSA reduces to minimizing a local
smooth function. Local linear convergence then holds under certain conditions.
We determine the rate in terms of the inertia, stepsize, and local curvature.
Our local analysis is applicable to certain recent variants of the Fast
Iterative Shrinkage-Thresholding Algorithm (FISTA), for which we establish
active manifold identification and local linear convergence. Our analysis
motivates the use of a momentum restart scheme in these FISTA variants to
obtain the optimal local linear convergence rate.

34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg