Journal of Applied Mathematics

Journal of Applied Mathematics / 2003 / Article

Open Access

Volume 2003 |Article ID 836784 | https://doi.org/10.1155/S1110757X03301081

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

Received23 Jan 2003
Revised09 Apr 2003

Abstract

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.

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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