Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Inexact Proximal Path-Following Algorithm for Constrained Convex
  Minimization   Many scientific and engineering applications feature nonsmooth convex
minimization problems over convex sets. In this paper, we address an important
instance of this broad class where we assume that the nonsmooth objective is
equipped with a tractable proximity operator and that the convex constraint set
affords a self-concordant barrier. We provide a new joint treatment of proximal
and self-concordant barrier concepts and illustrate that such problems can be
efficiently solved, without the need of lifting the problem dimensions, as in
disciplined convex optimization approach. We propose an inexact path-following
algorithmic framework and theoretically characterize the worst-case analytical
complexity of this framework when the proximal subproblems are solved
inexactly. To show the merits of our framework, we apply its instances to both
synthetic and real-world applications, where it shows advantages over standard
interior point methods. As a by-product, we describe how our framework can
obtain points on the Pareto frontier of regularized problems with
self-concordant objectives in a tuning free fashion.

30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
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
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th