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Abstract: Karmarkar's 1984 paper has produced a resurgence of interest in logarithmic barrier methods for linear and nonlinear programming. Although barrier methods for nonlinear inequality-constrained optimization were widely applied throughout the 1960's, they were largely abandoned in favor of other approaches during the 1970's. This shift was partly caused by the inefficiency of "black-box" methods in solving the unconstrained subproblems. Some of these difficulties were explained by results of... (Update)
Context of citations to this paper: More
...conditioning is one of the factors that led to the decline in popularity of barrier methods in the 1970s. Recently, it was proved in [Wr92b] that the barrier Hessian is ill conditioned in an entire neighborhood of x . Although this property might appear to imply that the...
...and Liu [1] Forsgren, Gill, and Shinnerl [2] Gill, Saunders, and Shinnerl [4] Gould [7] Murray [9] Nash and Sofer [10] M. Wright [17], S. Wright [19] The differences between these other works and ours may be summarized as follows. These other works typically look...
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5: Interior methods for constrained optimization - Wright - 1992
4: A barrier method for large-scale constrained optimization (context) - Nash, Sofer - 1991
4: Practical Optimization (context) - Gill, Murray et al. - 1981
BibTeX entry: (Update)
M. H. Wright, Determining subspace information from the Hessian of a barrier function, Report NAM 92-02, AT&T Bell Laboratories, Murray Hill, New Jersey, 1992. http://citeseer.ist.psu.edu/wright92determining.html More
@techreport{ wright92determining,
author = "M. H. Wright",
title = "Determining subspace information from the {Hessian} of a barrier function",
number = "92--02",
address = "Murray Hill, NJ~07974, USA",
year = "1992",
url = "citeseer.ist.psu.edu/wright92determining.html" }
Citations (may not include all citations):624 The Algebraic Eigenvalue Problem (context) - Wilkinson - 1965
482 Combinatorial Optimization: Algorithms and Complexity (context) - Papadimitriou, Steiglitz - 1982
448 A new polynomial time algorithm for linear programming (context) - Karmarkar - 1984
313 Matrix Perturbation Theory (context) - Stewart, Sun - 1990
64 Interior methods for constrained optimization - Wright - 1992
35 A new modified Cholesky factorization (context) - Schnabel, Eskow - 1990
15 A barrier method for large-scale constrained optimization (context) - Nash, Sofer - 1991
12 Analytical expressions for the eigenvalues and eigenvectors .. (context) - Murray - 1971
11 Hessian matrices of penalty functions for solving constraine.. (context) - Lootsma - 1969
10 Numerical Methods for Nonlinearly Constrained Optimization (context) - Wright - 1976
5 Projected Lagrangian methods based on the trajectories of pe.. (context) - Murray, Wright - 1978
The graph only includes citing articles where the year of publication is known.
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