AI helps discover counterexample to ADMM convergence

By PulseAugur Editorial · [1 sources] · 2026-08-17 04:00

Researchers have discovered a counterexample to the convergence of a specific type of three-block Alternating Direction Method of Multipliers (ADMM) when the third constraint block is an identity matrix. Utilizing AI tools like Codex with GPT-5.6 Sol, they constructed and verified an explicit rational counterexample that produces a bounded nonconvergent orbit. Further investigation with AI, including Kimi Code and Kimi K3, explored multiplier relaxation techniques to restore convergence, finding that a small dual step can be effective while no positive relative step works universally. AI

IMPACT Demonstrates AI's capability in advanced mathematical research and theorem discovery.

RANK_REASON The item is an arXiv preprint detailing a mathematical discovery aided by AI tools. [lever_c_demoted from research: ic=1 ai=1.0]

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AI helps discover counterexample to ADMM convergence

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arXiv cs.AI TIER_1 English(EN) · Kenan Xu, Xiangfeng Wang · 2026-08-17 04:00

AI-Assisted Discovery and Construction of a Counterexample to the Convergence of Three-Block ADMM with the Identity Matrix as its Third Constraint Block

arXiv:2608.14396v1 Announce Type: cross Abstract: The alternating direction method of multipliers (ADMM), as a landmark algorithm, has attracted tremendous research attention and extensive practical applications over the past two decades. It is well known that, although the two-b…

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AI-Assisted Discovery and Construction of a Counterexample to the Convergence of Three-Block ADMM with the Identity Matrix as its Third Constraint Block

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