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Operator splitting performance estimation : Tight contraction factors and optimal parameter selection

RYU, ERNEST K. ; TAYLOR, ADRIEN B. ; BERGELING, CAROLINA LU orcid and GISELSSON, PONTUS LU orcid (2020) In SIAM Journal on Optimization 30(3). p.2251-2271
Abstract

We propose a methodology for studying the performance of common splitting methods through semidefinite programming. We prove tightness of the methodology and demonstrate its value by presenting two applications of it. First, we use the methodology as a tool for computerassisted proofs to prove tight analytical contraction factors for Douglas-Rachford splitting that are likely too complicated for a human to find bare-handed. Second, we use the methodology as an algorithmic tool to computationally select the optimal splitting method parameters by solving a series of semidefinite programs.

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author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Computer-aided analyses, First-order methods, Monotone operators, Rates of convergence, Splitting methods
in
SIAM Journal on Optimization
volume
30
issue
3
pages
21 pages
publisher
Society for Industrial and Applied Mathematics
external identifiers
  • scopus:85091165188
ISSN
1052-6234
DOI
10.1137/19M1304854
language
English
LU publication?
yes
id
e2b4254b-876f-42b0-8f41-03591f65ee20
date added to LUP
2020-11-20 14:35:51
date last changed
2023-11-20 15:22:22
@article{e2b4254b-876f-42b0-8f41-03591f65ee20,
  abstract     = {{<p>We propose a methodology for studying the performance of common splitting methods through semidefinite programming. We prove tightness of the methodology and demonstrate its value by presenting two applications of it. First, we use the methodology as a tool for computerassisted proofs to prove tight analytical contraction factors for Douglas-Rachford splitting that are likely too complicated for a human to find bare-handed. Second, we use the methodology as an algorithmic tool to computationally select the optimal splitting method parameters by solving a series of semidefinite programs. </p>}},
  author       = {{RYU, ERNEST K. and TAYLOR, ADRIEN B. and BERGELING, CAROLINA and GISELSSON, PONTUS}},
  issn         = {{1052-6234}},
  keywords     = {{Computer-aided analyses; First-order methods; Monotone operators; Rates of convergence; Splitting methods}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{2251--2271}},
  publisher    = {{Society for Industrial and Applied Mathematics}},
  series       = {{SIAM Journal on Optimization}},
  title        = {{Operator splitting performance estimation : Tight contraction factors and optimal parameter selection}},
  url          = {{http://dx.doi.org/10.1137/19M1304854}},
  doi          = {{10.1137/19M1304854}},
  volume       = {{30}},
  year         = {{2020}},
}