New Interior-Point Algorithm for Symmetric Optimization Based on a Positive-Asymptotic Barrier Function. (18th November 2018)

• Record Type: Journal Article
• Authors: Darvay, Zsolt; Rigó, Petra Renáta
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 15(2018)
• Page Start: 1705
• Page End: 1726
• Publication Date: 2018-11-18
• Subjects: Euclidean Jordan algebra -- positive-asymptotic kernel function -- polynomial complexity -- symmetric cone -- symmetric optimization; 90C25 -- 90C51; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1492938
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: We define a new interior-point method (IPM), which is suitable for solving symmetric optimization (SO) problems. The proposed algorithm is based on a new search direction. In order to obtain this direction, we apply the method of algebraically equivalent transformation on the centering equation of the central path. We prove that the associated barrier cannot be derived from a usual kernel function. Therefore, we introduce a new notion, namely the concept of the positive-asymptotic kernel function. We conclude that this algorithm solves the problem in polynomial time and has the same complexity as the best known IPMs for SO.