Barzilai-Borwein Fails Superlinear Convergence on an Open Set of Quadratics for Every Dimension $n\geq 4$
Barzilai--Borwein (BB) method has shown strong practical performance in continuous optimization, yet its convergence dynamics remains poorly understood. In particular, a central unresolved question is whether BB converges superlinearly for almost every strictly convex quadratic problem and initialization. We provide a negative answer to this question. Specifically, for every finite dimension $n\geq4$, we construct a nonempty open, hence positive-Lebesgue-measure, family of strictly convex quadratic problems and initial points for which the long Barzilai--Borwein method (BB1) converges but cann
Lineage graph
Paper → model → repo connections mined from source citations (Tier-1 exact match).
Why these links exist
Every edge carries a method, confidence, and the source snippet that justified it — so bad links are debuggable.
- LinkedLinked via arxiv author · 85%Dawei Li →
“Barzilai-Borwein Fails Superlinear Convergence on an Open Set of Quadratics for Every Dimension $n\geq 4$”
- LinkedLinked via arxiv author · 85%Xiaotian Jiang →
“Barzilai-Borwein Fails Superlinear Convergence on an Open Set of Quadratics for Every Dimension $n\geq 4$”
- LinkedLinked via arxiv author · 85%Mingyi Hong →
“Barzilai-Borwein Fails Superlinear Convergence on an Open Set of Quadratics for Every Dimension $n\geq 4$”
- FuzzyOverlapping authors or contributors · 62%affaan-m/ECC →
“Shared author/contributor keys: jiang”
- FuzzyOverlapping authors or contributors · 62%BerriAI/litellm →
“Shared author/contributor keys: jiang”