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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

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