We prove the theoretical convergence of a short-step, approximate path-following, interior-point primal-dual algorithm for semidefinite programs based on the Gauss-Newton direction obtained from minimizing the norm of the perturbed optimality conditions. This is the first proof of convergence for the Gauss-Newton direction in this context. It assumes strict complementarity and uniqueness of the optimal solution as well as an estimate of the smallest singular value of the Jacobian.
Serge Kruk. Henry Wolkowicz. "Convergence of a short-step primal-dual algorithm based on the Gauss-Newton direction." J. Appl. Math. 2003 (10) 517 - 534, 24 September 2003. https://doi.org/10.1155/S1110757X03301081