Open Access
24 September 2003 Convergence of a short-step primal-dual algorithm based on the Gauss-Newton direction
Serge Kruk, Henry Wolkowicz
J. Appl. Math. 2003(10): 517-534 (24 September 2003). DOI: 10.1155/S1110757X03301081


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.


Download Citation

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.


Published: 24 September 2003
First available in Project Euclid: 29 September 2003

zbMATH: 1080.65537
MathSciNet: MR2013788
Digital Object Identifier: 10.1155/S1110757X03301081

Primary: 65K05 , 90C51
Secondary: 90C22

Rights: Copyright © 2003 Hindawi

Vol.2003 • No. 10 • 24 September 2003
Back to Top