NDLI: An Inexact Proximal Path-Following Algorithm for Constrained Convex Minimization

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Tran-Dinh, Quoc Cevher, Volkan Kyrillidis, Anastasios
Copyright Year	2014
Abstract	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 byproduct, we describe how our framework can obtain points on the Pareto frontier of regularized problems with self-concordant objectives in a tuning free fashion.
Starting Page	1718
Ending Page	1745
Page Count	28
File Format	PDF
ISSN	10526234
DOI	10.1137/130944539
e-ISSN	10957189
Journal	SIAM Journal on Optimization (SJOPE8)
Issue Number	4
Volume Number	24
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2014-10-16
Access Restriction	Subscribed
Subject Keyword	constrained convex optimization Applications of mathematical programming General inexact path-following algorithm self-concordant barrier Interior-point methods proximal-Newton method Convex programming tractable proximity
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Software

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