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Math paper challenges Rockafellar's sum conjecture with operator examples

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This paper presents mathematical counterexamples to Rockafellar's sum conjecture, specifically addressing the behavior of maximally monotone operators. The authors construct examples on the spaces $c_0$ and $\ell^1$ where two such operators satisfy the interior-domain condition, yet their sum does not exhibit maximal monotonicity. A general construction theorem is introduced to compute the monotone polar of certain graphs and establish conditions for maximal monotonicity, which is then applied to generate the counterexample on $c_0$. Additionally, a bounded linear surjection is used to derive the counterexample for $\ell^1$. The work includes formalizations of the $c_0$ counterexample and a related lemma in Lean. AI

RANK_REASON The item is a research paper submitted to arXiv cs.LG. [lever_c_demoted from research: ic=1 ai=0.1]

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Math paper challenges Rockafellar's sum conjecture with operator examples

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The item is a research paper submitted to arXiv cs.LG. [lever_c_demoted from research: ic=1 ai=0.1]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Weifeng Yang ·

    Nonmaximal sums of maximally monotone operators under Rockafellar's constraint qualification

    arXiv:2609.10487v2 Announce Type: replace Abstract: We construct counterexamples to Rockafellar's sum conjecture in which two maximally monotone operators satisfy the interior-domain condition but their sum is not maximally monotone. We give one counterexample on $c_0$ and anothe…

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