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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 popularly 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 wikiPageRevisionID "594645356".
- Cutting-plane_method hasPhotoCollection Cutting-plane_method.
- Cutting-plane_method subject Category:Optimization_algorithms_and_methods.
- Cutting-plane_method type Abstraction100002137.
- Cutting-plane_method type Act100030358.
- Cutting-plane_method type Activity100407535.
- Cutting-plane_method type Algorithm105847438.
- Cutting-plane_method type Event100029378.
- Cutting-plane_method type OptimizationAlgorithmsAndMethods.
- Cutting-plane_method type Procedure101023820.
- Cutting-plane_method type PsychologicalFeature100023100.
- Cutting-plane_method type Rule105846932.
- Cutting-plane_method type YagoPermanentlyLocatedEntity.
- 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 popularly 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 label "Méthode des plans sécants".
- Cutting-plane_method label "Método de planos de corte".
- Cutting-plane_method label "Método de planos de corte".
- Cutting-plane_method label "Schnittebenenverfahren".
- Cutting-plane_method label "Алгоритм Гомори".
- 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 Q1762039.
- Cutting-plane_method sameAs Q1762039.
- Cutting-plane_method sameAs Cutting-plane_method.
- Cutting-plane_method wasDerivedFrom Cutting-plane_method?oldid=594645356.
- Cutting-plane_method isPrimaryTopicOf Cutting-plane_method.