Operator splitting performance estimation : Tight contraction factors and optimal parameter selection
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/e2b4254b-876f-42b0-8f41-03591f65ee20
- author
- RYU, ERNEST K. ; TAYLOR, ADRIEN B. ; BERGELING, CAROLINA LU and GISELSSON, PONTUS LU
- organization
- publishing date
- 2020
- 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}}, }