Reduction Algorithm for Pairs of Convex Polytopes
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Date
2015-01
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Addis Ababa University
Abstract
Qusidi_Erentiable Optimization Plays A Vital Role In The Study Of Non Smooth
Optimization Problems. The Quasidi_Erential Of A Quasidi_Erentiable Function
Is A Pair Of Compact Convex Sets In A Locally Convex Topological Vector
Space, Which Are Not Uniquely Determined. Due To The Non Uniqueness Of
The Quasidi_Erentials There Is A Great Interest In _Nding A Minimal Pair By
De_Ning An Equivalence Class. In Particular, The Quasidi_Erential Of A Piece
Wise Linear Function Is A Pair Of Convex Polytopes. For The Case Of Two Dimensional
Polytopes, The Problem Of _Nding Minimal Pairs Is Entirely Solved
But The Case Of Higher Dimensions Is Still Open.
In Di_Erent Papers It Was Given Some Theoretical Results On Reduction Methods
For Pair Of Compact Convex Sets Using Cutting Hyperplanes But Still There
Is No Set Of Instructions Or An Algorithm That Helps To Implement This Task.
Particularly, In This Paper We Will De_Ne What By Mean Reducible And Nonreducible
Pairs Of Polytopes And Develop An Algorithm That Can Reduce Any
Pair Of Polytopes To An Equivalent Non-Reducible Pair Of Polytopes Via Cutting
Hyperplanes, But Not Necessarily Minimal
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Qusidierentiable optimization plays a vital role in the study