Optimization Online


On the connection of facially exposed, and nice cones

Gabor Pataki(gabor***at***unc.edu)

Abstract: A closed convex cone K is called nice, if the set K^* + F^\perp is closed for all F faces of K, where K^* is the dual cone of K, and F^\perp is the orthogonal complement of the linear span of F. The niceness property plays a role in the facial reduction algorithm of Borwein and Wolkowicz, and the question whether the linear image of a nice cone is closed also has a simple answer. We prove several characterizations of nice cones and show a strong connection with facial exposedness. We prove that a nice cone must be facially exposed; in reverse, facial exposedness with an added technical condition implies niceness. We conjecture that nice, and facially exposed cones are actually the same, and give some supporting evidence.

Keywords: facially exposed cones, nice cones

Category 1: Convex and Nonsmooth Optimization

Category 2: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 3: Linear, Cone and Semidefinite Programming (Semi-definite Programming )


Download: [PDF]

Entry Submitted: 09/23/2011
Entry Accepted: 09/23/2011
Entry Last Modified: 09/23/2011

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