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- Interior_point_method abstract "Interior point methods (also referred to as barrier methods) are a certain class of algorithms to solve linear and nonlinear convex optimization problems.The interior point method was invented by John von Neumann. Von Neumann suggested a new method of linear programming, using the homogeneous linear system of Gordan (1873) which was later popularized by Karmarkar's algorithm, developed by Narendra Karmarkar in 1984 for linear programming. The method consists of a self-concordant barrier function used to encode the convex set. Contrary to the simplex method, it reaches an optimal solution by traversing the interior of the feasible region.Any convex optimization problem can be transformed into minimizing (or maximizing) a linear function over a convex set by converting to the epigraph form. The idea of encoding the feasible set using a barrier and designing barrier methods was studied by Anthony V. Fiacco, Garth P. McCormick, and others in the early 1960s. These ideas were mainly developed for general nonlinear programming, but they were later abandoned due to the presence of more competitive methods for this class of problems (e.g. sequential quadratic programming).Yurii Nesterov and Arkadi Nemirovski came up with a special class of such barriers that can be used to encode any convex set. They guarantee that the number of iterations of the algorithm is bounded by a polynomial in the dimension and accuracy of the solution.Karmarkar's breakthrough revitalized the study of interior point methods and barrier problems, showing that it was possible to create an algorithm for linear programming characterized by polynomial complexity and, moreover, that was competitive with the simplex method.Already Khachiyan's ellipsoid method was a polynomial time algorithm; however, in practice it was too slow to be of practical interest.The class of primal-dual path-following interior point methods is considered the most successful.Mehrotra's predictor-corrector algorithm provides the basis for most implementations of this class of methods[citation needed].".
- Interior_point_method thumbnail Karmarkar.png?width=300.
- Interior_point_method wikiPageExternalLink pg=537.
- Interior_point_method wikiPageExternalLink cvxbook.
- Interior_point_method wikiPageID "1622862".
- Interior_point_method wikiPageRevisionID "597401260".
- Interior_point_method hasPhotoCollection Interior_point_method.
- Interior_point_method subject Category:Optimization_algorithms_and_methods.
- Interior_point_method type Abstraction100002137.
- Interior_point_method type Act100030358.
- Interior_point_method type Activity100407535.
- Interior_point_method type Algorithm105847438.
- Interior_point_method type Event100029378.
- Interior_point_method type OptimizationAlgorithmsAndMethods.
- Interior_point_method type Procedure101023820.
- Interior_point_method type PsychologicalFeature100023100.
- Interior_point_method type Rule105846932.
- Interior_point_method type YagoPermanentlyLocatedEntity.
- Interior_point_method comment "Interior point methods (also referred to as barrier methods) are a certain class of algorithms to solve linear and nonlinear convex optimization problems.The interior point method was invented by John von Neumann. Von Neumann suggested a new method of linear programming, using the homogeneous linear system of Gordan (1873) which was later popularized by Karmarkar's algorithm, developed by Narendra Karmarkar in 1984 for linear programming.".
- Interior_point_method label "Innere-Punkte-Verfahren".
- Interior_point_method label "Interior point method".
- Interior_point_method label "Méthodes de points intérieurs".
- Interior_point_method label "内点法".
- Interior_point_method sameAs Innere-Punkte-Verfahren.
- Interior_point_method sameAs Méthodes_de_points_intérieurs.
- Interior_point_method sameAs 内点法.
- Interior_point_method sameAs m.05hg2j.
- Interior_point_method sameAs Q461992.
- Interior_point_method sameAs Q461992.
- Interior_point_method sameAs Interior_point_method.
- Interior_point_method wasDerivedFrom Interior_point_method?oldid=597401260.
- Interior_point_method depiction Karmarkar.png.
- Interior_point_method isPrimaryTopicOf Interior_point_method.
