primal-dual path-following algorithms for circular programming

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.