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A note on the condition numbers of convex sets

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Abstract

In this note, we give a counterexample to show that the characterization formula for the condition numbers of a convex set \(C\) of \(\mathbb R^n\) given in Coulibaly and Crouzeix (Math Program 116:79–113, 2009) is incorrect.

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References

  1. Coulibaly, A., Crouzeix, J.-P.: Condition numbers and error bounds in convex programming. Math. Program. 116, 79–113 (2009)

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Authors and Affiliations

  1. School of Mathematical Sciences, Harbin Normal University, Harbin, 150025, China

    Wen Song & Xiaomei Xu

  2. Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung, 807, Taiwan

    Jen-Chih Yao

  3. Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Jen-Chih Yao

Authors
  1. Wen Song
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  2. Xiaomei Xu
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  3. Jen-Chih Yao
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Corresponding author

Correspondence to Wen Song.

Additional information

W. Song: The research of this author was partly supported by the National Natural Sciences Grant (No. 11071052).

X. Xu: The research of this author was partly supported by the graduate students innovate scientific research program of Heilongjiang Province in 2009.

J.-C. Yao: The research of this author was partly supported by NSC 102-2115-M-037-002-MY3.

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Song, W., Xu, X. & Yao, JC. A note on the condition numbers of convex sets. Math. Program. 149, 459–463 (2015). https://doi.org/10.1007/s10107-014-0758-0

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  • DOI: https://doi.org/10.1007/s10107-014-0758-0

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