Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 2 2 2017 09 01 Primal-dual path-following algorithms for circular programming 65 85 13631 10.22049/cco.2017.25865.1051 EN Baha Alzalg The University of Jordan Mohammad Pirhaji Shahrekord University Journal Article 2017 01 23 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. https://comb-opt.azaruniv.ac.ir/article_13631_3b92d66c63867691344b503a2f0746f7.pdf