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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... (Update)
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BibTeX entry: (Update)
R. D. C. Monteiro. Polynomial convergence of primal-dual algorithms for semidefinite programming based on Monteiro and Zhang family of directions. Working paper, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA, July 1996. http://citeseer.ist.psu.edu/article/monteiro97polynomial.html More
@article{ monteiro00polynomial,
author = "R. D. C. Monteiro and T. Tsuchiya",
title = "Polynomial Convergence of Primal-Dual Algorithms for the Second-Order Cone Program Based on the {MZ}-Family of Directions",
journal = "Mathematical Programming",
volume = "88(1)",
pages = "61--83",
year = "2000",
url = "citeseer.ist.psu.edu/article/monteiro97polynomial.html" }
Citations (may not include all citations):708 Cambridge University Press (context) - Horn, Johnson et al. - 1985
230 Interior point methods in semidefinite programming with appl.. - Alizadeh - 1995
173 An interior-point method for semidefinite programming - Helmberg, Rendl et al. - 1996
146 Primal-dual interior-point methods for semidefinite programm.. - Alizadeh, Haeberly et al. - 1994
142 Primal-dual interior-point methods for self-scaled cones - Nesterov, Todd - 1995
140 Interior path-following primal-dual algorithms (context) - Monteiro, Adler - 1989
99 Primal-dual path following algorithms for semidefinite progr.. - Monteiro - 1995
92 the Nesterov-Todd direction in semidefinite programming - Todd, Toh et al. - 1996
90 A primal-dual potential reduction method for problems involv.. - Vandenberghe, Boyd - 1995
85 A primal--dual interior point algorithm for linear programmi.. (context) - Kojima, Mizuno et al. - 1989
85 On adaptive step primal--dual interior--point algorithms for.. (context) - Mizuno, Todd et al. - 1993
78 Interior-point methods for the monotone semidefinite linear .. (context) - Kojima, Shindoh et al. - 1997
73 A polynomial-time algorithm for a class of linear complement.. (context) - Kojima, Mizuno et al. - 1989
55 Symmetric primal-dual path-following algorithms for semidefi.. - Sturm, Zhang - 1995
49 An interior-point method for minimizing the maximum eigenval.. (context) - Jarre - 1993
47 A superlinearly convergent primal-dual infeasible-interior-p.. - Potra, Sheng - 1995
40 A unified analysis for a class of path-following primaldual .. (context) - Monteiro, Zhang - 1996
40 Superlinear convergence of a symmetric primal-dual path-foll.. - Luo, Sturm et al. - 1996
34 On extending some primal--dual interior--point algorithms fr.. - Zhang - 1995
30 Local convergence of predictor-corrector infeasibleinterior .. - Kojima, Shida et al. - 1995
25 Complexity of an algorithm for finding an approximate soluti.. (context) - Freund - 1994
18 Search directions and convergence analysis of some infeasibl.. - Tseng - 1996
17 A predictor-corrector method for semi-definite programming (context) - Lin, Saigal - 1995
14 A class of projective transformations for linear programming (context) - Ye - 1990
12 A note on the existence of the Alizadeh-HaeberlyOverton dire.. - Monteiro, Zanjacomo - 1996
8 A general approach to the design of optimal methods for smoo.. (context) - Nesterov, Nemirovskii - 1988
6 Society for Industrial and Applied Mathematics (context) - Methods, Programming et al. - 1994
4 Part II: Convex quadratic programming (context) - primal-dual - 1989
4 Central Economic & Mathematical Institute (context) - functions, methods et al. - 1989
3 Tokyo Institute of Technology (context) - on, Nesterov-Todd et al. - 1996
3 Central Economic & Mathematical Institute (context) - positive, matrices et al. - 1990
3 Tokyo Institute of Technology (context) - interior-point, semidefinite et al. - 1996
2 Mathematics of Operations Research (context) - barriers, for et al. - 1997
1 Courant Institute of Mathematical Sciences (context) - methods, programming et al. - 1996
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Documents on the same site (http://www.isye.gatech.edu/~monteiro/iplist.html): More
A Potential Reduction Newton Method for Constrained Equations - Monteiro, Pang (1999) (Correct)
Polynomiality of Primal-Dual Algorithms for Semidefinite.. - Monteiro, Tsuchiya (1997) (Correct)
A Superlinear Infeasible-Interior-Point Affine Scaling.. - Monteiro, Wright (1993) (Correct)
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