English(EN) Nonmaximal sums of maximally monotone operators under Rockafellar's constraint qualification

数学论文用算子示例挑战Rockafellar的和猜想

作者 PulseAugur 编辑部 · [1 个来源] · 2026-09-15 04:00

本文提出了Rockafellar和猜想的数学反例，特别关注极大单调算子的行为。作者在$c_0$和$\ell^1$空间上构造了两个这样的算例，它们满足内域条件，但它们的和并不表现出极大单调性。引入了一个通用的构造定理来计算某些图的单调极和建立极大单调性的条件，然后将其应用于在$c_0$上生成反例。此外，使用有界线性满射来推导$\ell^1$的反例。该工作包括$c_0$反例的正式化以及Lean中的相关引理。 AI

排序理由该条目是提交到arXiv cs.LG的研究论文。[lever_c_demoted from research: ic=1 ai=0.1]

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arXiv cs.LG TIER_1 English(EN) · Weifeng Yang · 2026-09-15 04:00

Rockafellar约束条件下，极大单调算子的非极大值和

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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Rockafellar约束条件下，极大单调算子的非极大值和

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