The Q method for second order cone programming

We develop the Q method for the second order cone programming problem. The algorithm is the adaptation of the Q method for semidefinite programming originally developed by Alizadeh, Haeberly and Overton [A new primal–dual interior point method for semidefinite programming. In: Proceedings of the fifth SIAM conference on applications of linear algebra, Snowbird, Utah, 1994.] and [Primal–dual interior-point methods for semidefinite programming: convergence rates, stability and numerical results. SIAM Journal on Optimization 1998;8(3):746–68 [electronic].]. We take advantage of the special algebraic structure associated with second order cone programs to formulate the Q method. Furthermore we discuss the convergence properties of the algorithm. Finally, some numerical results are presented.