Title of Poster / Presentation

The Smallest Intersecting Ball Problem

Presentation Type

Poster

Location

Portland State University, Portland, Oregon

Start Date

5-12-2015 11:00 AM

End Date

5-12-2015 1:00 PM

Subjects

Mathematical optimization, Convex functions

Abstract

The smallest intersecting ball problem involves finding the minimal radius necessary to intersect a collection of closed convex sets. This poster discusses relevant tools of convex optimization and explores three methods of finding the optimal solution: the subgradient method, log-exponential smoothing, and an original approach using target set expansion. A fourth algorithm based on weighted projections is given, but its convergence is yet unproven. Numerical tests and comparison between methods are also presented.

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Persistent Identifier

http://archives.pdx.edu/ds/psu/15374

Included in

Mathematics Commons

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May 12th, 11:00 AM May 12th, 1:00 PM

The Smallest Intersecting Ball Problem

Portland State University, Portland, Oregon

The smallest intersecting ball problem involves finding the minimal radius necessary to intersect a collection of closed convex sets. This poster discusses relevant tools of convex optimization and explores three methods of finding the optimal solution: the subgradient method, log-exponential smoothing, and an original approach using target set expansion. A fourth algorithm based on weighted projections is given, but its convergence is yet unproven. Numerical tests and comparison between methods are also presented.