Convergence of Three-Block ADMM with Identity Third Block
Statement
After Chen-He-Ye-Yuan's counterexample to direct three-block ADMM, the subclass in which the third constraint block is the identity matrix remained unresolved: the literature contained neither a convergence proof nor a counterexample. Disproved: an explicit rational counterexample exists in which the first two blocks are strongly convex quadratics and direct three-block ADMM produces a bounded nonconvergent orbit of period 66, verified by exact checks along a piecewise-affine reduction path.
Record
Comments
No person has examined this. Nothing here has been checked at all. say whether it holds →
construction · #1
Kenan Xu and Xiangfeng Wang, using GPT-5.6 Sol (Codex)That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
The paper is framed as AI-assisted discovery in its own title: using Codex with GPT-5.6 Sol, the authors construct the explicit rational counterexample candidate and verify it along a piecewise-affine reduction path, with exact checks establishing the period-66 nonconvergent orbit; the same Codex workflow guides a further study.
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