- The automorphism group and the non-self-duality of p-cones Masaru Ito (ito.mmath.cst.nihon-u.ac.jp) Bruno F. Lourenco (lourencomist.i.u-tokyo.ac.jp) Abstract: In this paper, we determine the automorphism group of the p-cones (p\neq 2) in dimension greater than two. In particular, we show that the automorphism group of those p-cones are the positive scalar multiples of the generalized permutation matrices that fix the main axis of the cone. Next, we take a look at a problem related to the duality theory of the p-cones. Under the Euclidean inner product it is well-known that a p-cone is self-dual only when p=2. However, it was not known whether it is possible to construct an inner product depending on p which makes the p-cone self-dual. Our results shows that no matter which inner product is considered, a p-cone will never become self-dual unless p=2 or the dimension is less than three. Keywords: p-cone, automorphism group, self-duality Category 1: Linear, Cone and Semidefinite Programming Category 2: Convex and Nonsmooth Optimization Citation: Download: [PDF]Entry Submitted: 06/28/2018Entry Accepted: 06/28/2018Entry Last Modified: 08/05/2018Modify/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.