Acyclic Monotone Operators Are Not Closed Under Addition
Henry Shugart
TL;DR
This paper demonstrates that the set of acyclic monotone operators is not closed under addition, answering a question posed by Borwein and Wiersma.
Contribution
It provides a negative answer to whether acyclic monotone operators are closed under addition, clarifying a previously open theoretical question.
Findings
Acyclic monotone operators are not closed under addition.
The paper resolves an open question from Borwein and Wiersma.
Provides a counterexample or proof for the non-closure.
Abstract
Borwein and Wiersma [SIAM J. Optim. 18(3) (2007), 946-960] asked if the set of acyclic monotone operators is closed under addition. We answer this question in the negative.
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