Journal of Applied Mathematics
Volume 2003 (2003), Issue 10, Pages 517-534
Convergence of a short-step primal-dual algorithm based on the Gauss-Newton direction
1Department of Mathematics and Statistics, Oakland University, Rochester 48309, MI, USA
2Department of Combinatorics and Optimization, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada
Received 23 January 2003; Revised 9 April 2003
Copyright © 2003 Serge Kruk and Henry Wolkowicz. 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.
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.