期刊
SIAM JOURNAL ON OPTIMIZATION
卷 30, 期 3, 页码 2251-2271出版社
SIAM PUBLICATIONS
DOI: 10.1137/19M1304854
关键词
computer-aided analyses; first-order methods; rates of convergence; monotone operators; splitting methods
资金
- NSF [DMS-1720237]
- ONR [N000141712162]
- European Research Council (ERC) under the European Union [724063]
- Swedish Foundation for Strategic Research
- Swedish Research Council
- European Research Council (ERC) [724063] Funding Source: European Research Council (ERC)
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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