Convergence of a short-step primal-dual algorithm based on the Gauss-Newton direction
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 th...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/S1110757X03301081 |
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| _version_ | 1849684933759467520 |
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| author | Serge Kruk Henry Wolkowicz |
| author_facet | Serge Kruk Henry Wolkowicz |
| author_sort | Serge Kruk |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-bc865cd9efab4d52b35e9ac62b72e733 |
| institution | DOAJ |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-bc865cd9efab4d52b35e9ac62b72e7332025-08-20T03:23:19ZengWileyJournal of Applied Mathematics1110-757X1687-00422003-01-0120031051753410.1155/S1110757X03301081Convergence of a short-step primal-dual algorithm based on the Gauss-Newton directionSerge Kruk0Henry Wolkowicz1Department of Mathematics and Statistics, Oakland University, Rochester 48309, MI, USADepartment of Combinatorics and Optimization, University of Waterloo, Waterloo N2L 3G1, Ontario, CanadaWe 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.http://dx.doi.org/10.1155/S1110757X03301081 |
| spellingShingle | Serge Kruk Henry Wolkowicz Convergence of a short-step primal-dual algorithm based on the Gauss-Newton direction Journal of Applied Mathematics |
| title | Convergence of a short-step primal-dual algorithm based on the Gauss-Newton direction |
| title_full | Convergence of a short-step primal-dual algorithm based on the Gauss-Newton direction |
| title_fullStr | Convergence of a short-step primal-dual algorithm based on the Gauss-Newton direction |
| title_full_unstemmed | Convergence of a short-step primal-dual algorithm based on the Gauss-Newton direction |
| title_short | Convergence of a short-step primal-dual algorithm based on the Gauss-Newton direction |
| title_sort | convergence of a short step primal dual algorithm based on the gauss newton direction |
| url | http://dx.doi.org/10.1155/S1110757X03301081 |
| work_keys_str_mv | AT sergekruk convergenceofashortstepprimaldualalgorithmbasedonthegaussnewtondirection AT henrywolkowicz convergenceofashortstepprimaldualalgorithmbasedonthegaussnewtondirection |