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Abstract: This paper establishes the polynomial convergence of a new class of primal-dual interior-point path following feasible algorithms for semidefinite programming (SDP) whose search directions are obtained by applying Newton method to the symmetric central path equation (PXP T ) 1=2 (P \GammaT SP \Gamma1 )(P XP T ) 1=2 \Gamma ¯I = 0; where P is a nonsingular matrix. Specifically, we show that the short-step path following algorithm based on the Frobenius norm neighborhood and the... (Update)
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...Monteiro y and Paulo R. Zanj acomo y July 10, 1997 Revised on August 4, 1997 Abstract Monteiro and Tsuchiya [23] have proposed two primal dual Newton directions for semidefinite programming, referred to as the MT directions, and established polynomial convergence of path...
...and some serious solvers (for example, Borchers [6] and Fujisawa and Kojima [11] use this direction only. 1.2. The MT Direction. Monteiro and Tsuchiya [24] apply Newton s method to the system obtained from (3) 6) by replacing (6) with 0. The resulting direction is guaranteed...
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BibTeX entry: (Update)
R. Monteiro and T. Tsuchiya. Polynomial Convergence of a New Family of Primal-Dual Algorithms for Semidefinite Programming. Technical Report 627, The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106, Japan, November 1996. http://citeseer.ist.psu.edu/article/monteiro98polynomial.html More
@article{ monteiro99polynomial,
author = "R. D. C. Monteiro and T. Tsuchiya",
title = "Polynomial Convergence of a New Family of Primal-Dual Algorithms for Semidefinite Programming",
journal = "SIAM Journal on Optimization",
volume = "9(3)",
pages = "551--577",
year = "1999",
url = "citeseer.ist.psu.edu/article/monteiro98polynomial.html" }
Citations (may not include all citations):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
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 Superlinear convergence of a symmetric primal-dual path-foll.. - Luo, Sturm et al. - 1996
40 A unified analysis for a class of path-following primaldual .. (context) - Monteiro, Zhang - 1996
39 Polynomial convergence of primal-dual algorithms for semidef.. - Monteiro - 1996
34 On extending some primal--dual interior--point algorithms fr.. - Zhang - 1995
31 the search directions in interior-point methods for semidefi.. (context) - Todd - 1997
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 Implementation of primal-dual methods for semidefinite progr.. - Monteiro, Zanj'acomo - 1997
14 A class of projective transformations for linear programming (context) - Ye - 1990
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
5 Complementarity-enforcing centered Newton method for mathema.. (context) - Tanabe - 1987
4 Central Economic & Mathematical Institute (context) - functions, methods et al. - 1989
4 Part II: Convex quadratic programming (context) - primal-dual - 1989
3 Tokyo Institute of Technology (context) - interior-point, the et al. - 1996
3 Central Economic & Mathematical Institute (context) - positive, matrices et al. - 1990
3 Tokyo Institute of Technology (context) - on, Nesterov-Todd et al. - 1996
2 SIAM Journal on Optimization (context) - following, semidefinite - 1997
2 Mathematics of Operations Research (context) - barriers, for et al. - 1997
1 Reports on Computational Mathematics (context) - local, of et al. - 1997
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Documents on the same site (http://www.isye.gatech.edu/~monteiro/iplist.html): More
Polynomial Convergence of Primal-Dual Algorithms for.. - Monteiro (1997) (Correct)
A Potential Reduction Newton Method for Constrained Equations - Monteiro, Pang (1999) (Correct)
Polynomiality of Primal-Dual Algorithms for Semidefinite.. - Monteiro, Tsuchiya (1997) (Correct)
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