A Note on the Paper “The Algebraic Structure of the Arbitrary-Order Cone”

Xin He Miao, Yen chi Roger Lin, Jein Shan Chen

研究成果: 雜誌貢獻期刊論文同行評審

3 引文 斯高帕斯(Scopus)

摘要

In this short paper, we look into a conclusion drawn by Alzalg (J Optim Theory Appl 169:32–49, 2016). We think the conclusion drawn in the paper is incorrect by pointing out three things. First, we provide a counterexample that the proposed inner product does not satisfy bilinearity. Secondly, we offer an argument why a pth-order cone cannot be self-dual under any reasonable inner product structure on Rn. Thirdly, even under the assumption that all elements operator commute, the inner product becomes an official inner product and the arbitrary-order cone can be shown as a symmetric cone, we think this condition is still unreasonable and very stringent so that the result can only be applied to very few cases.

原文英語
頁(從 - 到)1066-1070
頁數5
期刊Journal of Optimization Theory and Applications
173
發行號3
DOIs
出版狀態已發佈 - 2017 六月 1

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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