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Abstract: Interior methods are a central, striking feature of the constrained optimization landscape today, but it was not always so. Primarily in the form of barrier methods, interiorpoint techniques were widely used during the 1960s to solve nonlinearly constrained problems. However, their use for linear programming was not even contemplated because of the total dominance of the simplex method. During the 1970s, barrier methods were superseded by newly emerging, apparently more efficient... (Update)
Context of citations to this paper: More
.... of interior point methods for nonlinear programming ( 79] 3] 1] 2] 20] 47] 78] 12] 31] 70] 74] 82] 76] [80]) Several promising new algorithms have been proposed, and are being developed into high quality software ( 77] 12] 84] Not...
.... x k 1 of BS( k ) is found, the parameter k is updated and attention turns to the next barrier subproblem (see for instance [6, 16, 18] for a general survey and [19] for the linear case) Under reasonable conditions [2, 6, 16] it can be shown that the sequence fx k g...
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Sensitivity Analysis And The Analytic Central Path - Holder (1998) (Correct)
Interior-Point Methods - Terlaky, Boggs (Correct)
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0.5: Active Set and Interior Methods for Nonlinear Optimization - Byrd, Nocedal (Correct)
0.5: Properties of the Log-Barrier Function on Degenerate Nonlinear .. - Wright, Orban (1999) (Correct)
0.5: On the Convergence of the Newton/Log-Barrier Method - Wright (2001) (Correct)
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0.3: Optimization Methods For Base Station Placement In Wireless.. - Wright (1998) (Correct)
0.1: An Interior-Point Algorithm for the Maximum-Volume Ellipsoid Problem - Zhang (1999) (Correct)
0.1: Recent Developments In Interior-point Methods - Wright (1999) (Correct)
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4: Primal-Dual Interior-Point Methods (context) - Wright - 1997
3: Practical Optimization (context) - Gill, Murray et al. - 1981
2: A Polynomial algorithm in linear programming (context) - Khachiyan - 1979
BibTeX entry: (Update)
M. H. Wright. The interior-point revolution in constrained optimization. Technical Report 98-4-09, Computing Sciences Research Center, Bell Laboratories, Murray Hill, New Jersey 07974, USA, June 1998. http://citeseer.ist.psu.edu/wright98interiorpoint.html More
@incollection{ wright98interiorpoint,
author = "M. H. Wright",
title = "The interior-point revolution in constrained optimization",
booktitle = "High-Performance Algorithms and Software in Nonlinear Optimization",
publisher = "Kluwer Academic Publishers",
editor = "R. DeLeone and A. Murli and P. M. Pardalos and G. Toraldo",
pages = "359--381",
year = "1998",
url = "citeseer.ist.psu.edu/wright98interiorpoint.html" }
Citations (may not include all citations):717 Theory of Linear and Integer Programming (context) - Schrijver - 1987
686 Practical Methods of Optimization (context) - Fletcher - 1987
663 Practical Optimization (context) - Gill, Murray et al. - 1981
529 Linear Matrix Inequalities in System and Control Theory (context) - Boyd, Ghaoui et al. - 1994
482 Iterative Solution of Nonlinear Equations in Several Variabl.. (context) - Ortega, Rheinboldt - 1970
448 A new polynomial time algorithm for linear programming (context) - Karmarkar - 1984
415 Improved approximation algorithms for maximum cut and satisf.. - Goemans, Williamson - 1995
326 Interior-Point Polynomial Algorithms in Convex Programming (context) - Nesterov, Nemirovskii - 1994
186 Primal-Dual Interior-Point Methods (context) - Wright - 1996
146 Primal-dual interior-point methods for semidefinite programm.. - Alizadeh, Haeberly et al. - 1996
115 Introduction to Linear and Nonlinear Programming (context) - Luenberger - 1973
85 Path following methods for linear programming (context) - Gonzaga - 1992
64 Interior methods for constrained optimization - Wright - 1992
63 Linear Programming (context) - Chv'atal - 1983
57 Eigenvalue optimization - Lewis, Overton - 1996
57 Theory and Algorithms for Linear Optimization: An Interior P.. (context) - Roos, Terlaky et al. - 1997
47 the formulation and theory of the Newton interior-point meth.. (context) - El-Bakry, Tapia et al. - 1996
47 A trust region method based on interior point techniques for.. - Byrd, Gilbert et al. - 1996
42 Primal-dual interior methods for nonconvex nonlinear program.. (context) - Forsgren, Gill - 1996
36 A primal-dual interior method for nonconvex nonlinearly cons.. (context) - Gay, Overton et al. - 1998
35 Department of Operations Research (context) - Murtagh, Saunders et al. - 1987
34 Numerical Linear Algebra and Optimization (context) - Gill, Murray et al. - 1991
34 On projected Newton barrier methods for linear programming a.. (context) - Gill, Murray et al. - 1986
22 Linear programming (context) - Goldfarb, Todd - 1989
19 Interior Point Algorithms (context) - Ye - 1997
18 Stability of symmetric ill-conditioned systems arising in in.. (context) - Forsgren, Gill et al. - 1996
18 Linear Programming: Foundations and Extensions - Vanderbei - 1997
16 A note on using alternative second-order models for the subp.. - Conn, Gould et al. - 1994
16 Why a pure primal Newton barrier step may be infeasible - Wright - 1995
15 the use of directions of negative curvature in a modified Ne.. (context) - Mor'e, Sorensen - 1979
15 Ill-conditioning and computational error in interior methods.. (context) - Wright - 1997
13 Modified Cholesky factorizations in interior-point algorithm.. - Wright - 1996
12 Analytical expressions for the eigenvalues and eigenvectors .. (context) - Murray - 1971
11 Hessian matrices of penalty functions for solving constraine.. (context) - Lootsma - 1969
11 Stability of linear equation solvers in interior-point metho.. - Wright - 1995
10 Computing modified Newton directions using a partial Cholesk.. (context) - Forsgren, Gill et al. - 1995
8 Some properties of the Hessian of the logarithmic barrier fu.. (context) - Wright - 1994
5 Stability of augmented system factorizations in interior-poi.. - Wright - 1997
2 Finite-precision effects on the local convergence of interio.. (context) - Wright - 1998
1 Treating indefiniteness in nonconvex nonlinearly constrained.. (context) - Gay, Overton et al. - 1998
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Approximability and Nonapproximability Results for.. - Kellerer.. (1995) (Correct)
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