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

Kruk, Serge; Wolkowicz, Henry

J. Appl. Math., Tome 2003 (2003) no. 1, p. 517-534 / Harvested from Project Euclid

Résumé

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.

Publié le : 2003-09-24
Classification: 65K05, 90C51, 90C22

@article{1064850345,
     author = {Kruk, Serge and Wolkowicz, Henry},
     title = {Convergence of a short-step primal-dual algorithm based on the Gauss-Newton direction},
     journal = {J. Appl. Math.},
     volume = {2003},
     number = {1},
     year = {2003},
     pages = { 517-534},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1064850345}
}

Kruk, Serge; Wolkowicz, Henry. Convergence of a short-step primal-dual algorithm based on the Gauss-Newton direction. J. Appl. Math., Tome 2003 (2003) no. 1, pp.  517-534. http://gdmltest.u-ga.fr/item/1064850345/