Reduction Algorithm for Pairs of Convex Polytopes
| dc.contributor.advisor | Mitiku, Semu (PhD) | |
| dc.contributor.author | Worku, Getnet | |
| dc.date.accessioned | 2018-07-16T07:22:01Z | |
| dc.date.accessioned | 2023-11-04T12:32:24Z | |
| dc.date.available | 2018-07-16T07:22:01Z | |
| dc.date.available | 2023-11-04T12:32:24Z | |
| dc.date.issued | 2015-01 | |
| dc.description.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 | en_US |
| dc.identifier.uri | http://etd.aau.edu.et/handle/123456789/8646 | |
| dc.language.iso | en | en_US |
| dc.publisher | Addis Ababa University | en_US |
| dc.subject | Qusidierentiable optimization plays a vital role in the study | en_US |
| dc.title | Reduction Algorithm for Pairs of Convex Polytopes | en_US |
| dc.type | Thesis | en_US |