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

Ernest Ryu (1) , Adrien Taylor (2) , Carolina Bergeling (3) , Pontus Giselsson (3)

1 Department of Mathematical Sciences [Seoul]
2 SIERRA - Statistical Machine Learning and Parsimony
3 Department of Automatic Control

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.

Domaines: Optimisation et contrôle [math.OC]

Ernest Ryu, Adrien Taylor, Carolina Bergeling, Pontus Giselsson. Operator Splitting Performance Estimation: Tight Contraction Factors and Optimal Parameter Selection. SIAM Journal on Optimization, 2020, 30 (3), pp.2251-2271. ⟨10.1137/19M1304854⟩. ⟨hal-02956361⟩