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Operator Splitting Performance Estimation: Tight Contraction Factors and Optimal Parameter Selection

Ernest Ryu 1 Adrien Taylor 2 Carolina Bergeling 3 Pontus Giselsson 3
2 SIERRA - Statistical Machine Learning and Parsimony
DI-ENS - Département d'informatique de l'École normale supérieure, CNRS - Centre National de la Recherche Scientifique, Inria de Paris
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 computer-assisted 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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Submitted on : Wednesday, October 7, 2020 - 12:18:50 PM
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Ernest Ryu, Adrien Taylor, Carolina Bergeling, Pontus Giselsson. Operator Splitting Performance Estimation: Tight Contraction Factors and Optimal Parameter Selection. SIAM Journal on Optimization, Society for Industrial and Applied Mathematics, 2020, 30 (3), pp.2251-2271. ⟨10.1137/19M1304854⟩. ⟨hal-02956361⟩

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