Serge Kruk, Henry Wolkowicz, "Convergence of a short-step primal-dual algorithm based on the Gauss-Newton direction", Journal of Applied Mathematics, vol. 2003, Article ID 836784, 18 pages, 2003. https://doi.org/10.1155/S1110757X03301081
Convergence of a short-step primal-dual algorithm based on the Gauss-Newton direction
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.
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