Journal of Applied Mathematics 
Volume 2003 (2003), Issue 10, Pages 517-534
doi:10.1155/S1110757X03301081

Convergence of a short-step primal-dual algorithm based on the Gauss-Newton direction

Serge Kruk1 and Henry Wolkowicz2

 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

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.