-

 

 

 




Optimization Online





 

On self-concordant barriers for generalized power cones

Scott Roy(scott.michael.roy***at***gmail.com)
Lin Xiao(lin.xiao***at***microsoft.com)

Abstract: In the study of interior-point methods for nonsymmetric conic optimization and their applications, Nesterov introduced the power cone, together with a 4-self-concordant barrier for it. In his PhD thesis, Chares found an improved 3-self-concordant barrier for the power cone. In addition, he introduced the generalized power cone, and conjectured a nearly optimal self-concordant barrier for it. In this short note, we prove Chares’ conjecture. As a byproduct of our analysis, we derive a self-concordant barrier for a high-dimensional nonnegative power cone.

Keywords: interior-point methods, nonsymmetric cones, self-concordant barriers

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Linear, Cone and Semidefinite Programming (Other )

Citation: Microsoft Research Technical Report: MSR-TR-2018-3

Download: [PDF]

Entry Submitted: 01/30/2018
Entry Accepted: 01/30/2018
Entry Last Modified: 01/30/2018

Modify/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
Mathematical Optimization Society