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Abstract: A new approach for the implementation of interior-point methods for solving linear programs is proposed. Its main feature is the iterative solution of the symmetric, but highly indefinite 2\Theta2-block systems of linear equations that arise within the interior-point algorithm. These linear systems are solved by a symmetric variant of the quasi-minimal residual (QMR) algorithm, which is an iterative solver for general linear systems. The symmetric QMR algorithm can be combined with indefinite... (Update)
Context of citations to this paper: More
.... problem is computed simultaneously with the solution of the inverse problem (cf. 28] In this paper, a variant of symmetric QMR [16, 15] is employed and an effective preconditioner is obtained by solving the reduced Hessian system approximately. Since the reduced Hessian...
...the search directions are calculated exactly. Algorithms featuring similar search directions were proposed by Freund, Jarre and Mizuno (see [1], 2] and [8] After some basic notes and definitions (x2) we give a motivation for the use of inexact search directions and state our...
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0.5: Preconditioning of Symmetric, but Highly Indefinite Linear Systems - Freund (1997) (Correct)
0.4: Software for simplified Lanczos and QMR algorithms - Freund, Nachtigal (1995) (Correct)
0.3: A New Krylov-Subspace Method For Symmetric Indefinite Linear.. - Freund, Nachtigal (1994) (Correct)
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0.4: Solving the Sum-of-Ratios Problem by an Interior-Point Method - Freund, Jarre (1999) (Correct)
0.3: QMR: a Quasi-Minimal Residual Method for Non-Hermitian.. - Freund, Nachtigal (1991) (Correct)
0.3: An Interior-Point Method For Convex Fractional Programming - Freund, Jarre (1993) (Correct)
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8: Computational experience with a primal-dual interior point method for linear pro.. (context) - Lustig, Marsten et al. - 1991
7: A new polynomial time algorithm for linear programming (context) - Karmarkar - 1984
6: Electronic mail distribution of linear programming test problems (context) - Gay - 1985
BibTeX entry: (Update)
Roland W. Freund, Florian Jarre, A QMR-Based Interior-Point Algorithm for Solving Linear Programs, Numerical Analysis Manuscript 94-19, AT&T Bell Laboratories, December 1994, to appear in Math. Programming, Series B http://citeseer.ist.psu.edu/freund94qmrbased.html More
@article{ freund96qmrbased,
author = "R. W. Freund and F. Jarre",
title = "A {QMR}-based interior-point algorithm for solving linear programs",
journal = "Mathematical Programming, Series~B",
volume = "76",
pages = "183--210",
year = "1996",
url = "citeseer.ist.psu.edu/freund94qmrbased.html" }
Citations (may not include all citations):448 A new polynomial-time algorithm for linear programming (context) - Karmarkar - 1984
318 Methods of conjugate gradients for solving linear systems (context) - Hestenes, Stiefel - 1952
257 QMR: a quasi-minimal residual method for non-Hermitian linea.. - Freund, Nachtigal - 1991
159 An implementation of the look-ahead Lanczos algorithm for no.. - Freund, Gutknecht et al. - 1993
151 Iterative solution of linear systems - Freund, Golub et al. - 1992
142 Solution of sparse indefinite systems of linear equations (context) - Paige, Saunders - 1975
140 Interior path following primal-dual algorithms, Part I: Line.. (context) - Monteiro, Adler - 1989
101 Pathways to the optimal set in linear programming (context) - Megiddo - 1989
92 Electronic mail distribution of linear programming test prob.. (context) - Gay - 1985
85 A primal-dual interior point algorithm for linear programmin.. (context) - Kojima, Mizuno et al. - 1989
62 Computational experience with a primal-dual interior point m.. (context) - Lustig, Marsten et al. - 1991
54 On implementing Mehrotra's predictor-corrector interior-poin.. (context) - Lustig, Marsten et al. - 1992
49 An implementation of the QMR method based on coupled two-ter.. - Freund, Nachtigal - 1994
44 Direct methods for solving symmetric indefinite systems of l.. (context) - Bunch, Parlett - 1971
40 Efficient implementation of a class of preconditioned conjug.. (context) - Eisenstat - 1981
40 Preconditioners for indefinite systems arising in optimizati.. (context) - Gill, Murray et al. - 1992
35 Symmetric indefinite systems for interior point methods (context) - Vanderbei, Carpenter - 1993
35 An implementation of Karmarkar's algorithm for linear progra.. - Adler, Karmarkar et al. - 1989
34 A primal-dual infeasible-interior-point algorithm for linear.. (context) - Kojima, Megiddo et al. - 1993
30 Solving symmetric indefinite systems in an interior-point me.. (context) - Fourer, Mehrotra - 1993
29 Computational results of an interior point algorithm for lar.. (context) - Karmarkar, Ramakrishnan - 1991
27 A survey of preconditioned iterative methods for linear syst.. (context) - Axelsson - 1985
26 A simplified homogeneous and self-dual linear programming al.. (context) - Xu, Hung et al. - 1993
21 Transpose-free quasi-minimal residual methods for non-Hermit.. (context) - Freund - 1994
19 Centered Newton method for mathematical programming (context) - Tanabe - 1988
16 Quasi-kernel polynomials and convergence results for quasi-m.. (context) - Freund - 1992
11 Convergence of a class of inexact interior-point algorithms .. - Freund, Jarre et al. - 1996
10 Simplifications of the nonsymmetric Lanczos process and a ne.. (context) - Freund, Zha - 1995
9 A transpose-free quasi-minimal residual squared algorithm fo.. (context) - Freund, Szeto - 1992
2 Numerical experiences with a QMR-based interior-point algori.. (context) - Freund, Jarre - 1996
1 Implementation of a primal-dual path following method for so.. (context) - Menniken - 1991
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