Optimization Online


On the irreducibility, Lyapunov rank, and automorphisms of speical Bishop-Phelps cones

M. Seetharama Gowda(gowda***at***math.umbc.edu)
David Trott(dtrott1***at***umbc.edu)

Abstract: Motivated by optimization considerations, we consider special Bishop-Phelps cones in R^n which are of the form {(t,x): t \geq ||x||} for some norm on R^(n-1). We show that for n bigger than 2, such cones are always irreducible. De fining the Lyapunov rank of a proper cone K as the dimension of the Lie algebra of the automorphism group of K, we show that the Lyapunov rank of any special Bishop-Phelps polyhedral cone is one. Extending an earlier known result for the l_1 cone (which is a special Bishop-Phelps cone with 1-norm), we show that any l_p cone, for p different from 2, has Lyapunov rank one. We also study automorphisms of special Bishop-Phelps cones, in particular giving a complete description of the automorphisms of the l_1 cone.

Keywords: Complementarity set, Lyapunov rank, Bishop-Phelps cone, Irreducible cone

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Complementarity and Variational Inequalities

Citation: Research Report TRGOW13-01, Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, Maryland 21250, USA. August 2013

Download: [PDF]

Entry Submitted: 10/16/2013
Entry Accepted: 10/16/2013
Entry Last Modified: 10/16/2013

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society