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

Masaru Ito (ito.m***at***math.cst.nihon-u.ac.jp)
Bruno F. Lourenco (lourenco***at***st.seikei.ac.jp)

Abstract: 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.

Keywords: homogeneous cone, p-cone, T-algebra

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Convex and Nonsmooth Optimization

Citation: Masaru Ito, Bruno F. Lourenšo, 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

Download: [PDF]

Entry Submitted: 12/24/2016
Entry Accepted: 12/24/2016
Entry Last Modified: 08/22/2017

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