Masakazu Kojima, Nimron Megiddo, Shinji Mizuno  Home/Search
Context Related
| math.tau.ac.il/~megiddo...kmm2rev.ps.gz stanford.edu/~megiddo/....kmm2rev.ps.gz Cached: PS.gz PS PDF This document uses CoBlitz to cache paper downloads. If your firewall is blocking outgoing connections to port 3125, you can use these links to download local copies.
Image Update HelpPS.gz PS PDF From: math.tau.ac.il/~megiddo/pub (more) From: stanford.edu/~megiddo/pub (Enter author homepages) |
Rate this article:      (best)Comment on this article |
Abstract: . This paper proposes two sets of rules, Rule G and Rule P, for controlling step lengths in a generic primal-dual interior point method for solving the linear programming problem in standard form and its dual. Theoretically, Rule G ensures the global convergence, while Rule P, which is a special case of Rule G, ensures the O(nL) iteration polynomial-time computational complexity. Both rules depend only on the lengths of the steps from the current iterates in the primal and dual spaces to the... (Update)
Context of citations to this paper: More
.... following methods [32, 49] some long step path following algorithms [19, 20, 26] long step primal dual path following methods [30], and primal dual potential reduction algorithms [34, 63, 74] As shown in [24] all these algorithms either explicitly generate a...
.... path, see, e.g. Kojima, Mizuno and Noma (1990b) Kojima, Mizuno and Yoshise (1991d) Kojima, Megiddo and Noma (1991b) Kojima, Megiddo and Mizuno (1990a) Mizuno (1992) We present the Lemke algorithm as an example of a piecewise linear algorithm since it played a crucial...
Cited by: More
Interior-Point Methods for Linear Optimization - Roos (2000) (Correct)
Polynomiality of Primal-Dual Affine Scaling.. - Jansen, Roos.. (1995) (Correct)
A Quadratically Convergent Polynomial Long-Step Algorithm For A.. - Sun, Zhao (1999) (Correct)
Similar documents (at the sentence level):
49.4%: Theoretical Convergence of Large-Step Primal-Dual.. - Masakazu Kojima Nimrod (1992) (Correct)
Active bibliography (related documents): More All
1.1: A Unified ApproachtoInterior Point Algorithms - For Linear Complementarity (Correct)
1.1: A Unified Approach to Interior Point Algorithms for.. - Kojima, Megiddo.. (1991) (Correct)
0.6: An Infeasible-Interior-Point Potential-Reduction Algorithm for .. - Reha Tutuncu (1999) (Correct)
Similar documents based on text: More All
0.6: A Conjugate Direction Method for Approximating the.. - Masakazu Kojima Nimrod (1991) (Correct)
0.5: A General Framework of Continuation Methods for.. - Masakazu Kojima Nimrod (1994) (Correct)
0.5: Horizontal and Vertical Decomposition in Interior Point.. - Masakazu Kojima Nimrod (1993) (Correct)
Related documents from co-citation: More All
7: On Adaptive-Step Primal-Dual Interior-Point Algorithms for Linear Programming (context) - Mizuno, Todd et al. - 1993
6: Large steps path--following methods for linear programming, Part I : Barrier fun.. (context) - Gonzaga - 1991
4: Iterative solution of problems of linear and quadratic programming (context) - Dikin - 1967
BibTeX entry: (Update)
M. Kojima, N. Megiddo and S. Mizuno,"Theoretical convergence of large-step primaldual interior point algorithms for linear programming", Mathematical Programming, 59 (1992) 1-21. http://citeseer.ist.psu.edu/article/kojima92theoretical.html More
@article{ kojima93theoretical,
author = "M. Kojima and N. Megiddo and S. Mizuno",
title = "Theoretical convergence of large--step--primal--dual interior point algorithms for linear programming",
journal = "Mathematical Programming",
volume = "59",
pages = "1--21",
year = "1993",
url = "citeseer.ist.psu.edu/article/kojima92theoretical.html" }
Citations (may not include all citations):172 Nonlinear Programming: Sequential Unconstrained Minimization.. (context) - Fiacco, McCormick - 1968
140 Interior path following primal-dual algorithms, Part I: Line.. (context) - Monteiro, Adler - 1989
140 Interior path following primal-dual algorithms, Part II: Con.. (context) - Monteiro, Adler - 1989
116 A unified approach to interior point algorithms for linear c.. - Kojima, Megiddo et al. - 1990
101 Pathways to the optimal set in linear programming (context) - Megiddo - 1989
98 the implementation of a (primal-dual) interior point method (context) - Mehrotra - 1990
85 A primal-dual interior point algorithm for linear programmin.. (context) - Kojima, Mizuno et al. - 1989
85 On adaptive-step primal-dual interior-point algorithms for l.. (context) - Mizuno, Todd et al. - 1989
79 Iterative solution of problems of linear and quadratic progr.. (context) - Dikin - 1967
73 A polynomial-time algorithm for a class of linear complement.. (context) - Kojima, Mizuno et al. - 1989
46 A variation on Karmarkar's algorithm for solving linear prog.. (context) - Barnes - 1986
43 the superlinear and quadratic convergence of primal-dual int.. (context) - Zhang, Tapia et al. - 1990
41 A polynomial-time primal-dual affine scaling algorithm for l.. - Monteiro, Adler et al. - 1990
40 A modification of Karmarkar's linear programming algorithm (context) - Vanderbei, Meketon et al. - 1986
40 Homotopy continuation methods for nonlinear complementarity .. - Kojima, Megiddo et al.
35 An implementation of Karmarkar 's algorithm for linear progr.. - Adler, Resende et al. - 1989
34 An implementation of a primaldual interior point method for .. (context) - McShane, Monma et al. - 1989
21 A centered projective algorithm for linear programming (context) - Todd, Ye - 1990
19 Centered Newton method for mathematical programming (context) - Tanabe - 1988
17 Polynomial-time algorithms for linear programming based only.. (context) - Freund - 1988
14 Interior point methods for linear programming: Just call New.. (context) - Marsten, Subramanian et al. - 1990
13 An interior point potential reduction algorithm for the line.. - Kojima, Megiddo et al.
12 An O( p nL) iteration potential reduction algorithm for line.. (context) - Kojima, Mizuno et al. - 1991
11 the superlinear convergence of interior point algorithms for.. (context) - Zhang, Tapia et al. - 1990
10 An O(n 3 L) potential reduction algorithm for linear program.. (context) - Ye - 1991
8 Practical polynomial time algorithms for linear complementar.. (context) - Mizuno, Yoshise et al. - 1989
7 Global ellipsoidal approximations and homotopy methods for s.. (context) - Sonnevend, Stoer - 1988
5 Complementarity-enforcing centered Newton method for mathema.. (context) - Tanabe - 1987
4 A polynomial-time predictor-corrector algorithm for linear c.. (context) - Ding, Li - 1991
3 Private communication (context) - Lustig - 1989
3 Near-boundary behavior of primal-dual potential reduction al.. (context) - Ye, Kortanek et al. - 1990
3 Line search in potential reduction algorithms for linear pro.. - Ye - 1989
2 Optimal 3-dimensional methods for linear programming (context) - Domich, Boggs et al. - 1989
1 An O(n 3 L) algorithm using a sequence for a linear compleme.. (context) - Mizuno - 1990
1 A generic primal-dual interior point algorithm (context) - Lustig - 1988
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://www.math.tau.ac.il/~megiddo/pub.html): More
A General NP-Completeness Theorem - Megiddo (1993) (Correct)
On the Complexity of Some Geometric Problems in Unbounded Dimension - Megiddo (1990) (Correct)
A Unified Approach to Interior Point Algorithms for.. - Kojima, Megiddo.. (1991) (Correct)
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC