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Cutting-plane_method abstract "In mathematical optimization, the cutting-plane method is an umbrella term for optimization methods which iteratively refine a feasible set or objective function by means of linear inequalities, termed cuts. Such procedures are commonly used to find integer solutions to mixed integer linear programming (MILP) problems, as well as to solve general, not necessarily differentiable convex optimization problems. The use of cutting planes to solve MILP was introduced by Ralph E. Gomory and Václav Chvátal.Cutting plane methods for MILP work by solving a non-integer linear program, the linear relaxation of the given integer program. The theory of Linear Programming dictates that under mild assumptions (if the linear program has an optimal solution, and if the feasible region does not contain a line), one can always find an extreme point or a corner point that is optimal. The obtained optimum is tested for being an integer solution. If it is not, there is guaranteed to exist a linear inequality that separates the optimum from the convex hull of the true feasible set. Finding such an inequality is the separation problem, and such an inequality is a cut. A cut can be added to the relaxed linear program. Then, the current non-integer solution is no longer feasible to the relaxation. This process is repeated until an optimal integer solution is found.Cutting-plane methods for general convex continuous optimization and variants are known under various names: Kelley's method, Kelley-Cheney-Goldstein method, and bundle methods. They are popularly used for non-differentiable convex minimization, where a convex objective function and its subgradient can be evaluated efficiently but usual gradient methods for differentiable optimization can not be used. This situation is most typical for the concave maximization of Lagrangian dual functions. Another common situation is the application of the Dantzig-Wolfe decomposition to a structured optimization problem in which formulations with an exponential number of variables are obtained. Generating these variables on demand by means of delayed column generation is identical to performing a cutting plane on the respective dual problem.".
Cutting-plane_method wikiPageExternalLink gomory.pdf.
Cutting-plane_method wikiPageExternalLink integerRioMPSjuly.pdf.
Cutting-plane_method wikiPageExternalLink AMP-Chapter-09.pdf.
Cutting-plane_method wikiPageID "1597680".
Cutting-plane_method wikiPageLength "7280".
Cutting-plane_method wikiPageOutDegree "34".
Cutting-plane_method wikiPageRevisionID "692973230".
Cutting-plane_method wikiPageWikiLink Benders_decomposition.
Cutting-plane_method wikiPageWikiLink Branch_and_bound.
Cutting-plane_method wikiPageWikiLink Branch_and_cut.
Cutting-plane_method wikiPageWikiLink Category:Optimization_algorithms_and_methods.
Cutting-plane_method wikiPageWikiLink Column_generation.
Cutting-plane_method wikiPageWikiLink Convex_hull.
Cutting-plane_method wikiPageWikiLink Convex_optimization.
Cutting-plane_method wikiPageWikiLink Dantzig–Wolfe_decomposition.
Cutting-plane_method wikiPageWikiLink Feasible_region.
Cutting-plane_method wikiPageWikiLink Gérard_Cornuéjols.
Cutting-plane_method wikiPageWikiLink Integer.
Cutting-plane_method wikiPageWikiLink Integer_programming.
Cutting-plane_method wikiPageWikiLink Lagrange_multiplier.
Cutting-plane_method wikiPageWikiLink Lift-and-project.
Cutting-plane_method wikiPageWikiLink Linear_programming.
Cutting-plane_method wikiPageWikiLink Linear_programming_relaxation.
Cutting-plane_method wikiPageWikiLink Mathematical_optimization.
Cutting-plane_method wikiPageWikiLink Mathematics.
Cutting-plane_method wikiPageWikiLink Nonlinear_programming.
Cutting-plane_method wikiPageWikiLink Ralph_E._Gomory.
Cutting-plane_method wikiPageWikiLink Simplex_algorithm.
Cutting-plane_method wikiPageWikiLink Subderivative.
Cutting-plane_method wikiPageWikiLink Subgradient_method.
Cutting-plane_method wikiPageWikiLink Václav_Chvátal.
Cutting-plane_method wikiPageWikiLinkText "Cutting-plane method".
Cutting-plane_method wikiPageWikiLinkText "Cutting-plane method#Gomory's cut".
Cutting-plane_method wikiPageWikiLinkText "Gomory's cut".
Cutting-plane_method wikiPageWikiLinkText "Gomory's mixed integer cuts".
Cutting-plane_method wikiPageWikiLinkText "cutting plane methods".
Cutting-plane_method wikiPageWikiLinkText "cutting planes".
Cutting-plane_method wikiPageWikiLinkText "cutting-plane method".
Cutting-plane_method wikiPageWikiLinkText "integer cuts".
Cutting-plane_method wikiPageUsesTemplate Template:Citation_needed.
Cutting-plane_method wikiPageUsesTemplate Template:Optimization_algorithms.
Cutting-plane_method subject Category:Optimization_algorithms_and_methods.
Cutting-plane_method hypernym Term.
Cutting-plane_method type Algorithm.
Cutting-plane_method comment "In mathematical optimization, the cutting-plane method is an umbrella term for optimization methods which iteratively refine a feasible set or objective function by means of linear inequalities, termed cuts. Such procedures are commonly used to find integer solutions to mixed integer linear programming (MILP) problems, as well as to solve general, not necessarily differentiable convex optimization problems. The use of cutting planes to solve MILP was introduced by Ralph E.".
Cutting-plane_method label "Cutting-plane method".
Cutting-plane_method sameAs Q1762039.
Cutting-plane_method sameAs Snitplansmetoden.
Cutting-plane_method sameAs Schnittebenenverfahren.
Cutting-plane_method sameAs Método_de_planos_de_corte.
Cutting-plane_method sameAs Méthode_des_plans_sécants.
Cutting-plane_method sameAs Método_de_planos_de_corte.
Cutting-plane_method sameAs m.05fgb1.
Cutting-plane_method sameAs Алгоритм_Гомори.
Cutting-plane_method sameAs Q1762039.
Cutting-plane_method wasDerivedFrom Cutting-plane_method?oldid=692973230.
Cutting-plane_method isPrimaryTopicOf Cutting-plane_method.