Primal-dual path-following algorithms for circular programming

• Main Authors: Baha Alzalg, ‎M‎. ‎Pirhaji
• Format: Article
• Language: English
• Published: Azarbaijan Shahide Madani University 2017-06-01
• Series: Communications in Combinatorics and Optimization
• Subjects: Circular cone programming‎; ‎Interior point methods‎; ‎Euclidean Jordan algebra‎; ‎Self-concordance
• Online Access: http://comb-opt.azaruniv.ac.ir/article_13631.html

Circular programming problems are a new class of convex optimization problems that include second-order cone programming problems as a special case‎. ‎Alizadeh and Goldfarb [Math‎. ‎Program‎. ‎Ser‎. ‎A 95 (2003) 3--51] introduced primal-dual path-following algorithms for solving second-order cone programming problems‎. ‎In this paper‎, ‎we generalize their work by using the machinery of Euclidean Jordan algebras associated with the circular cones to derive primal-dual path-following interior point algorithms for circular programming problems‎. ‎We prove polynomial convergence of the proposed algorithms by showing that the circular logarithmic barrier is a strongly self-concordant barrier‎. ‎The numerical examples show the path-following algorithms are simple and efficient‎.