%0 Journal Article
%T Primal-dual path-following algorithms for circular programming
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Alzalg, Baha
%A Pirhaji, Mohammad
%D 2017
%\ 09/01/2017
%V 2
%N 2
%P 65-85
%! Primal-dual path-following algorithms for circular programming
%K Circular cone programming
%K Interior point methods
%K Euclidean Jordan algebra
%K Self-concordance
%R 10.22049/cco.2017.25865.1051
%X 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.
%U http://comb-opt.azaruniv.ac.ir/article_13631_3b92d66c63867691344b503a2f0746f7.pdf