- The p-cones in dimension n>=3 are not homogeneous when p \neq 2 Masaru Ito (ito.mmath.cst.nihon-u.ac.jp) Bruno F. Lourenco (lourencost.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. 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 Download: [PDF]Entry Submitted: 12/24/2016Entry Accepted: 12/24/2016Entry Last Modified: 08/22/2017Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.