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arXiv · 2506.24076

The AutoLyap software suite for computer-assisted Lyapunov analyses of first-order methods

Manu Upadhyaya·Shuvomoy Das Gupta·Adrien B. Taylor·Sebastian Banert·Pontus Giselsson
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Abstract

We introduce AutoLyap, a software suite that assists with Lyapunov analyses of a wide class of first-order methods for structured optimization and inclusion problems. Lyapunov analyses are structured proof patterns, with historical roots in the study of dynamical systems, commonly used to establish convergence results for first-order methods. Building on previous work, the core idea behind AutoLyap is to recast the verification of the existence of a Lyapunov analysis as a semidefinite program (SDP), which can then be solved numerically using standard SDP solvers. Users of the package specify (i) the class of optimization or inclusion problems, (ii) the first-order method in question, and (iii) the type of Lyapunov analysis they wish to test. Once these inputs are provided, AutoLyap handles the SDP modeling and proceeds to solve the SDP numerically. We use the package to numerically verify and extend several convergence results. AutoLyap is currently available in Python and Julia.

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Manu Upadhyaya, Shuvomoy Das Gupta, Adrien B. Taylor, Sebastian Banert, Pontus Giselsson. 2025-06-30. The AutoLyap software suite for computer-assisted Lyapunov analyses of first-order methods. https://arxiv.org/abs/2506.24076

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