Polynomial Convergence of Primal-Dual Algorithms for Semidefinite Programming Based on Monteiro and Zhang Family of Directions (1997)
| Venue: | School of ISyE, Georgia Institute of Technology, Atlanta, GA 30332 |
| Citations: | 44 - 8 self |
BibTeX
@ARTICLE{Monteiro97polynomialconvergence,
author = {Renato D.C. Monteiro},
title = {Polynomial Convergence of Primal-Dual Algorithms for Semidefinite Programming Based on Monteiro and Zhang Family of Directions},
journal = {School of ISyE, Georgia Institute of Technology, Atlanta, GA 30332},
year = {1997},
volume = {88},
pages = {61--83}
}
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Abstract
This paper establishes the polynomialconvergence of the class of primal-dual feasible interiorpoint algorithms for semidefinite programming (SDP) based on Monteiro and Zhang family of search directions. In contrast to Monteiro and Zhang's work, no condition is imposed on the scaling matrix that determines the search direction. We show that the polynomial iterationcomplexity bounds of two well-known algorithms for linear programming, namely the short-step path-following algorithm of Kojima et al. and Monteiro and Adler, and the predictor-corrector algorithm of Mizuno et al., carry over to the context of SDP. Since Monteiro and Zhang family of directions includes the Alizadeh, Haeberly and Overton direction, we establish for the first time the polynomial convergence of algorithms based on this search direction. Keywords: Semidefinite programming, interior-point methods, polynomial complexity, pathfollowing methods, primal-dual methods. AMS 1991 subject classification: 65K05, 90C25, 90C...
