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Masaru Ito (ito.mmath.cst.nihonu.ac.jp) Abstract: Using the Talgebra machinery we show that the only strictly convex homogeneous cones in R^n with n >= 3 are the 2cones, also known as Lorentz cones or second order cones. In particular, this shows that the pcones 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, pcone, Talgebra Category 1: Linear, Cone and Semidefinite Programming Category 2: Convex and Nonsmooth Optimization Citation: Masaru Ito, Bruno F. Lourenço, The pcones in dimension n ≥ 3 are not homogeneous when p≠2, Linear Algebra and its Applications, Volume 533, 2017, Pages 326335, http://dx.doi.org/10.1016/j.laa.2017.07.029 Download: [PDF] Entry Submitted: 12/24/2016 Modify/Update this entry  
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