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The Ellipsoid Method: A Survey

In February 1979 a note by L. G. Khachiyan indicated how an ellipsoid method for linear programming can be implemented in polynomial time. This result has caused great excitement and stimulated a flood of technical papers. Ordinarily there would be no need for a survey of work so recent, but the cur... Full description

Journal Title: Operations research 1981-11-01, Vol.29 (6), p.1039-1091
Main Author: Bland, R.G
Other Authors: Goldfarb, D , Todd, M.J
Format: Electronic Article Electronic Article
Language: English
Subjects:
Publisher: Baltimore, Md: Operations Research Society of America
ID: ISSN: 0030-364X
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recordid: cdi_proquest_miscellaneous_23696551
title: The Ellipsoid Method: A Survey
format: Article
creator:
  • Bland, R.G
  • Goldfarb, D
  • Todd, M.J
subjects:
  • Algorithms
  • Analysis
  • Combinatorial optimization
  • Ellipsoids
  • Feature Article
  • Integers
  • Linear inequalities
  • Linear programming
  • Mathematical analysis
  • Mathematical inequalities
  • Methods
  • Operations Research
  • Polls & surveys
  • Polynomials
  • Simplex method
  • Surveys
ispartof: Operations research, 1981-11-01, Vol.29 (6), p.1039-1091
description: In February 1979 a note by L. G. Khachiyan indicated how an ellipsoid method for linear programming can be implemented in polynomial time. This result has caused great excitement and stimulated a flood of technical papers. Ordinarily there would be no need for a survey of work so recent, but the current circumstances are obviously exceptional. Word of Khachiyan's result has spread extraordinarily fast, much faster than comprehension of its significance. A variety of issues have, in general, not been well understood, including the exact character of the ellipsoid method and of Khachiyan's result on polynomiality, its practical significance in linear programming, its implementation, its potential applicability to problems outside of the domain of linear programming, and its relationship to earlier work. Our aim is to help clarify these important issues in the context of a survey of the ellipsoid method, its historical antecedents, recent developments, and current research.
language: eng
source:
identifier: ISSN: 0030-364X
fulltext: no_fulltext
issn:
  • 0030-364X
  • 1526-5463
url: Link


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descriptionIn February 1979 a note by L. G. Khachiyan indicated how an ellipsoid method for linear programming can be implemented in polynomial time. This result has caused great excitement and stimulated a flood of technical papers. Ordinarily there would be no need for a survey of work so recent, but the current circumstances are obviously exceptional. Word of Khachiyan's result has spread extraordinarily fast, much faster than comprehension of its significance. A variety of issues have, in general, not been well understood, including the exact character of the ellipsoid method and of Khachiyan's result on polynomiality, its practical significance in linear programming, its implementation, its potential applicability to problems outside of the domain of linear programming, and its relationship to earlier work. Our aim is to help clarify these important issues in the context of a survey of the ellipsoid method, its historical antecedents, recent developments, and current research.
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subjectAlgorithms ; Analysis ; Combinatorial optimization ; Ellipsoids ; Feature Article ; Integers ; Linear inequalities ; Linear programming ; Mathematical analysis ; Mathematical inequalities ; Methods ; Operations Research ; Polls & surveys ; Polynomials ; Simplex method ; Surveys
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abstractIn February 1979 a note by L. G. Khachiyan indicated how an ellipsoid method for linear programming can be implemented in polynomial time. This result has caused great excitement and stimulated a flood of technical papers. Ordinarily there would be no need for a survey of work so recent, but the current circumstances are obviously exceptional. Word of Khachiyan's result has spread extraordinarily fast, much faster than comprehension of its significance. A variety of issues have, in general, not been well understood, including the exact character of the ellipsoid method and of Khachiyan's result on polynomiality, its practical significance in linear programming, its implementation, its potential applicability to problems outside of the domain of linear programming, and its relationship to earlier work. Our aim is to help clarify these important issues in the context of a survey of the ellipsoid method, its historical antecedents, recent developments, and current research.
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pubOperations Research Society of America
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