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- Interior_point_method abstract "Interior point methods (also referred to as barrier methods) are a certain class of algorithms that solves linear and nonlinear convex optimization problems.John von Neumann suggested an interior point method of linear programming which was neither a polynomial time method nor an efficient method in practice. In fact, it turned out to be slower in practice compared to simplex method which is not a polynomial time method. In 1984, Narendra Karmarkar developed a method for linear programming called Karmarkar's algorithm which runs in provably polynomial time and is also very efficient in practice. It enabled solutions of linear programming problems which were beyond the capabilities of simplex method. Contrary to the simplex method, it reaches a best solution by traversing the interior of the feasible region. The method can be generalized to convex programming based on a self-concordant barrier function used to encode the convex set. 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, 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.".
- Interior_point_method thumbnail Karmarkar.svg?width=300.
- Interior_point_method wikiPageExternalLink cvxbook.
- Interior_point_method wikiPageExternalLink pg=537.
- Interior_point_method wikiPageID "1622862".
- Interior_point_method wikiPageLength "9079".
- Interior_point_method wikiPageOutDegree "38".
- Interior_point_method wikiPageRevisionID "671006442".
- Interior_point_method wikiPageWikiLink Algorithm.
- Interior_point_method wikiPageWikiLink Arkadi_Nemirovski.
- Interior_point_method wikiPageWikiLink Augmented_Lagrangian_method.
- Interior_point_method wikiPageWikiLink Barrier_function.
- Interior_point_method wikiPageWikiLink Candidate_solution.
- Interior_point_method wikiPageWikiLink Category:Optimization_algorithms_and_methods.
- Interior_point_method wikiPageWikiLink Convex_optimization.
- Interior_point_method wikiPageWikiLink Convex_set.
- Interior_point_method wikiPageWikiLink Diagonal_matrix.
- Interior_point_method wikiPageWikiLink Ellipsoid_method.
- Interior_point_method wikiPageWikiLink Epigraph.
- Interior_point_method wikiPageWikiLink Feasible_region.
- Interior_point_method wikiPageWikiLink Gradient.
- Interior_point_method wikiPageWikiLink Hessian_matrix.
- Interior_point_method wikiPageWikiLink Iteration.
- Interior_point_method wikiPageWikiLink Jacobian_matrix_and_determinant.
- Interior_point_method wikiPageWikiLink John_von_Neumann.
- Interior_point_method wikiPageWikiLink KKT_conditions.
- Interior_point_method wikiPageWikiLink Karmarkars_algorithm.
- Interior_point_method wikiPageWikiLink Karush–Kuhn–Tucker_conditions.
- Interior_point_method wikiPageWikiLink Lagrange_multiplier.
- Interior_point_method wikiPageWikiLink Leonid_Khachiyan.
- Interior_point_method wikiPageWikiLink Linear_function.
- Interior_point_method wikiPageWikiLink Linear_programming.
- Interior_point_method wikiPageWikiLink Mehrotra_predictor-corrector_method.
- Interior_point_method wikiPageWikiLink Mehrotra_predictor–corrector_method.
- Interior_point_method wikiPageWikiLink Narendra_Karmarkar.
- Interior_point_method wikiPageWikiLink Newton_method.
- Interior_point_method wikiPageWikiLink Newtons_method.
- Interior_point_method wikiPageWikiLink Nonlinear_optimization.
- Interior_point_method wikiPageWikiLink Nonlinear_programming.
- Interior_point_method wikiPageWikiLink Penalty_method.
- Interior_point_method wikiPageWikiLink Polynomial_time.
- Interior_point_method wikiPageWikiLink Self-concordant.
- Interior_point_method wikiPageWikiLink Self-concordant_function.
- Interior_point_method wikiPageWikiLink Sequential_quadratic_programming.
- Interior_point_method wikiPageWikiLink Simplex_algorithm.
- Interior_point_method wikiPageWikiLink Time_complexity.
- Interior_point_method wikiPageWikiLink Yurii_Nesterov.
- Interior_point_method wikiPageWikiLink File:Karmarkar.svg.
- Interior_point_method wikiPageWikiLinkText "Interior Point Method".
- Interior_point_method wikiPageWikiLinkText "Interior Point method".
- Interior_point_method wikiPageWikiLinkText "Interior point method".
- Interior_point_method wikiPageWikiLinkText "interior point method".
- Interior_point_method wikiPageWikiLinkText "interior point".
- Interior_point_method wikiPageWikiLinkText "interior-point solvers".
- Interior_point_method wikiPageWikiLinkText "interior-point techniques".
- Interior_point_method wikiPageWikiLinkText "path-following algorithm".
- Interior_point_method hasPhotoCollection Interior_point_method.
- Interior_point_method wikiPageUsesTemplate Template:Cite_book.
- Interior_point_method wikiPageUsesTemplate Template:Cite_journal.
- Interior_point_method wikiPageUsesTemplate Template:Optimization_algorithms.
- Interior_point_method wikiPageUsesTemplate Template:Reflist.
- Interior_point_method wikiPageUsesTemplate Template:Use_dmy_dates.
- Interior_point_method subject Category:Optimization_algorithms_and_methods.
- Interior_point_method hypernym Class.
- Interior_point_method type Article.
- Interior_point_method type Algorithm.
- Interior_point_method type Article.
- Interior_point_method comment "Interior point methods (also referred to as barrier methods) are a certain class of algorithms that solves linear and nonlinear convex optimization problems.John von Neumann suggested an interior point method of linear programming which was neither a polynomial time method nor an efficient method in practice. In fact, it turned out to be slower in practice compared to simplex method which is not a polynomial time method.".
- Interior_point_method label "Interior point method".
- 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 Метод_внутренней_точки.
- Interior_point_method sameAs Q461992.
- Interior_point_method sameAs Q461992.
- Interior_point_method wasDerivedFrom Interior_point_method?oldid=671006442.
- Interior_point_method depiction Karmarkar.svg.
- Interior_point_method isPrimaryTopicOf Interior_point_method.