On extending kernel-based interior point algorithms for linear programming to convex quadratic second-order cone programming

In this article, we extend kernel-based interior point algorithms for linear programming to convex quadratic programming overs second-order cones. By means of Jordan algebras, we establish the iteration complexity for long- and short-step interior-point methods, namely, O(³√(N₂) log N/ε ) and O(√N log N/ε), respectively. These results coincide with the ones obtained in the linear programming case.