On superlinear convergence of infeasible interior-point algorithms for linearly constrained convex programs

This note derives bounds on the length of the primal–dual affine scaling directions associated with a linearly constrained convex program satisfying the following conditions: (1) the problem has a solution satisfying strict complementarity, (2) the Hessian of the objective function satisfies a certain invariance property. We illustrate the usefulness of these bounds by establishing the superlinear convergence of the algorithm presented in Wright and Ralph for solving the optimality conditions associated with a linearly constrained convex program satisfying the above conditions.