Last-iterate convergence of optimistic gradient

This code comes jointly with reference

[1] "Last-Iterate Convergence of Optimistic Gradient Method for Monotone Variational Inequalities".

Date: May 2022

Requirements

Packages.

• To run our MATLAB code one should install Performance Estimation Toolbox (PESTO), SEDUMI (or any other appropriate SDP solver interfaced with YALMIP), YALMIP and add the to the path when executing our code.
• The Python codes for visualization require Jupyter notebooks.
• The Python codes for numerical verifications require Jupyter notebooks and PEPit (Performance Estimation in Python).

Organization of the code

The code is divided in four parts:

• PESTO codes for directly assessing the worst-case convergence speed of the methods under consideration, see folder PESTO_PastExtragradient_N_iterations).
• PESTO codes for verifying numerically Lemma 3.1, Lemma 4.1 as well as the potential functions from Theorem 1 and Theorem 2, see folder PESTO_PastExtragradient_potentials).
• PEPit codes (redundant with PESTO, but in Jupyter notebooks (Python)) for verifying numerically Lemma 3.1, Lemma 4.1 as well as the potential functions from Theorem 1 and Theorem 2, see folder PEPit_PastExtragradient_potentials).
• YALMIP codes for playing with the SDP formulations (less readable than PESTO codes but allows to go into the details), see folder DirectSDPs_Codes.