A Primal-dual Interior-point Algorithm for Symmetric Cone Convex Quadratic Programming Based on the Commutative Class Directions

In this paper, we present a neighborhood following primal-dual interior-point algorithm for solving symmetric cone convex quadratic programming problems, where the objective function is a convex quadratic function and the feasible set is the intersection of an affine subspace and a symmetric cone attached to a Euclidean Jordan algebra. The algorithm is based on the [13] broad class of commutative search directions for cone of semidefinite matrices, extended by [18] to arbitrary symmetric cones. Despite the fact that the neighborhood is wider, which allows the iterates move towards optimality with longer steps, the complexity iteration bound remains as the same result of Schmieta and Alizadeh for symmetric cone optimization problems.