Reduction Algorithm For Pairs Of Convex Polytopes

Qusidi_Erentiable Optimization Plays A Vital Role In The Study Of Non SmoothrnOptimization Problems. The Quasidi_Erential Of A Quasidi_Erentiable FunctionrnIs A Pair Of Compact Convex Sets In A Locally Convex Topological VectorrnSpace, Which Are Not Uniquely Determined. Due To The Non Uniqueness OfrnThe Quasidi_Erentials There Is A Great Interest In _Nding A Minimal Pair ByrnDe_Ning An Equivalence Class. In Particular, The Quasidi_Erential Of A PiecernWise Linear Function Is A Pair Of Convex Polytopes. For The Case Of Two DimensionalrnPolytopes, The Problem Of _Nding Minimal Pairs Is Entirely SolvedrnBut The Case Of Higher Dimensions Is Still Open.rnIn Di_Erent Papers It Was Given Some Theoretical Results On Reduction MethodsrnFor Pair Of Compact Convex Sets Using Cutting Hyperplanes But Still TherernIs No Set Of Instructions Or An Algorithm That Helps To Implement This Task.rnParticularly, In This Paper We Will De_Ne What By Mean Reducible And NonreduciblernPairs Of Polytopes And Develop An Algorithm That Can Reduce AnyrnPair Of Polytopes To An Equivalent Non-Reducible Pair Of Polytopes Via CuttingrnHyperplanes, But Not Necessarily Minimal

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