An optimal first-order method for smooth and strongly convex composite optimization and its stationary limit

This repository contains code for reproducing and verifying the main results of:

[1] Manu Upadhyaya, Daniel Berg Thomsen, Aymeric Dieuleveut, and Adrien Taylor. "An optimal first-order method for smooth and strongly convex composite optimization and its stationary limit," arXiv:2605.22929, 2026.

Authors

• Manu Upadhyaya
• Daniel Berg Thomsen
• Aymeric Dieuleveut
• Adrien Taylor

Repository Organization

• numerical_validation/prox_item_tmm_pepit.ipynb: PEPit worst-case analyses for finite-step Prox-ITEM and Prox-TMM bounds.
• numerical_validation/prox_item_autolyap.ipynb: AutoLyap iteration-dependent validation of the finite-horizon Prox-ITEM distance bound.
• numerical_validation/prox_tmm_autolyap.ipynb: AutoLyap iteration-independent validation of the stationary Prox-TMM rate.
• symbolic_verification/prox_item_lyapunov_sympy.ipynb: SymPy verification of the Prox-ITEM Lyapunov simplification.
• symbolic_verification/prox_tmm_lyapunov_sympy.ipynb: SymPy verification of the stationary Prox-TMM Lyapunov simplification.
• symbolic_verification/prox_item_proof_mathematica.nb: Mathematica verification of the Prox-ITEM proof reformulation.

Requirements

The Python notebooks require Jupyter with the packages used in each notebook:

• SymPy for symbolic verification.
• PEPit and NumPy for PEPit numerical validations.
• AutoLyap, NumPy, and Matplotlib for AutoLyap numerical validations.

The Mathematica notebook was created with Mathematica 13.3.