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Lyapunov Functions and $R$-Linear Convergence for Quadratic Barzilai-Borwein Dynamics

Year: 2026

Type: preprint

Abstract: The Barzilai--Borwein (BB) method is $R$-linearly convergent on strongly convex quadratics, although neither the objective value nor the gradient norm is generally monotone. We construct an explicit current-point Lyapunov function for the quadratic dynamics after the warm-up step, assuming that both endpoints of the initial active spectrum survive this step. If $a

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.12084

Authors: Yang, Shutai, Yuan, Ya-xiang

Institutions: University of Science and Technology of China, Chinese Academy of Sciences, Academy of Mathematics and Systems Science, State Key Laboratory of Scientific and Engineering Computing

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, University of Science and Technology of China, National College Students Innovation and Entrepreneurship Training Program

Award: G8533620077

OpenAlex ID: W7212652804

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