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: Serge Kruk, Henry Wolkowicz
Format: Article
Language:English
Published: Wiley 2003-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/S1110757X03301081
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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.
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issn 1110-757X
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publishDate 2003-01-01
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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