This code can be used to verify the theoretical statements from the monograph
[1] Alexandre d’Aspremont, Damien Scieur and Adrien Taylor (2021), "Acceleration Methods", Foundations and Trends® in Optimization: Vol. 5: No. 1-2, pp 1-245.
The arXiv version is available here, the Foundation and Trends version is available here.
Notes:
- Files in the folders
Proofs of Chapter 4/01_Symbolic
andProofs of Chapter 5/01_Symbolic
require Mathematica (for verifying analytical developments). - Files in the folders
Proofs of Chapter 4/02_Numerical
andProofs of Chapter 5/02_Numerical
require YALMIP along with a suitable SDP solver (e.g., Sedumi, SDPT3, Mosek), and the Performance Estimation Toolbox (PESTO). - Files in the folders
Proofs of Appendix C/
require Mathematica (for verifying analytical developments and performing the numerical experiments).
Proofs of Chapter 4
contains two subfolders.
01_Symbolic
contains Mathematica notebooks for verifying the algebraic manipulations required in the proof of the potential inequalities for the 14 gradient methods in this chapter.02_Numerical
contains Matlab codes for verifying the final bounds of the methods presented in the chapter.
Proofs of Chapter 5
contains two subfolders.
01_Symbolic
contains Mathematica notebooks for verifying the algebraic manipulations required in the proof of the potential inequalities for the 4 proximal methods in this chapter.02_Numerical
contains Matlab codes for verifying the final bounds of the 4 proximal methods presented in the chapter.
Proofs of Appendix C/
contains Mathematica notebooks for obtaining (analytically) and solving (numerically) the LMI formulations from Appendix C.