Work

Convergence analysis of dynamical systems for optimization by an improved Lyapunov framework

Year: 2026

Type: article

Abstract: We study the convergence analysis of continuous-time dynamical systems associated with optimization methods for strongly convex functions. Recent works have proposed systematic constructions of Lyapunov functions for such analysis, while also revealing limitations of the Lyapunov analysis. Aujol et al. (2023) have proposed a technique to address this issue by reorganizing Lyapunov functions so as to evaluate a quantity f(x(t)) − f* − g(t)‖x(t) − x*‖2 rather than f(x(t)) − f*. By combining this technique with our computer-assisted framework to discover Lyapunov functions, we develop an improved method that reproduces an existing convergence rate or yields better rates than previous studies.

Source: JSIAM Letters

DOI: 10.14495/jsiaml.18.117

Authors: Atsushi Tabei, Ken’ichiro Tanaka

Institutions: The University of Tokyo, Institute of Science Tokyo

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: Japan Society for the Promotion of Science

Award: New Development of Methods for Generating Sample Points by Variable Transformation