The p-cones in dimension n>=3 are not homogeneous when p \neq 2

  • Masaru Ito
  • Bruno F. Lourenço
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming Tags , , Short URL: https://optimization-online.org/?p=14333

    Using the T-algebra machinery we show that the only strictly convex homogeneous cones in R^n with n >= 3 are the 2-cones, also known as Lorentz cones or second order cones. In particular, this shows that the p-cones are not homogeneous when p is not 2, 1 < p <\infty and n >= 3, thus answering a problem proposed by Gowda and Trott.

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    Masaru Ito, Bruno F. Lourenço, The p-cones in dimension n ≥ 3 are not homogeneous when p≠2, Linear Algebra and its Applications, Volume 533, 2017, Pages 326-335, http://dx.doi.org/10.1016/j.laa.2017.07.029

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