Performance Estimation for Operator Splitting methods

This code comes jointly with the following reference.

[1] E. K. Ryu, A. B. Taylor, C. Bergeling, and P. Giselsson, "Operator Splitting Performance Estimation: Tight contraction factors and optimal parameter selection," SIAM Journal on Optimization 30 (3), 2251-2271, 2020

Date: December 3, 2018

Authors

• Ernest Ryu
• Adrien Taylor
• Carolina Bergeling
• Pontus Giselsson

Code

• (01) Symbolic verification of the algebra of Section C.1, the case where A is strongly monotone and B is cocoercive.

• (02) Symbolic verification of the algebra of Section C.2, the case where A is strongly monotone and B is Lipschitz monotone.

• (03) Numerical verification of the upper and lower bounds presented in Section C.1, the case where A is strongly monotone and B is cocoercive.

• (04) Numerical verification of the upper and lower bounds presented in Section C.2, the case where A is strongly monotone and B is Lipschitz monotone.

• (05) Numerical verification of the symmetry discussed in Remark 2, the case where A is Lipschitz monotone monotone and B is cocoercive.

• (06) Script implementing OSPEP for FBS, DRS, and DYS.

• (07) Code used to generate plots in Section 5.