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# An Algorithm for Computing the Symmetry Point of a Polytope

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 dc.contributor.author Belloni, Alexandre dc.contributor.author Freund, Robert M. dc.date.accessioned 2003-12-14T22:22:09Z dc.date.available 2003-12-14T22:22:09Z dc.date.issued 2004-01 dc.identifier.uri http://hdl.handle.net/1721.1/3876 dc.description.abstract Given a closed convex set C and a point x in C, let sym(x,C) denote the symmetry value of x in C, which essentially measures how symmetric C is about the point x. Denote by sym(C) the largest value of sym(x,C) among all x in C, and let x* denote the most symmetric point in C. These symmetry measures are all invariant under linear transformation, change in inner product, etc., and so are of interest in the study of the geometry of convex sets and arise naturally in the evaluation of the complexity of interior-point methods in particular. Herein we show that when C is given by the intersection of halfspaces, i.e., C={x | Ax <= b}, then x* as well as the symmetry value of C can be computed by using linear programming. Furthermore, given an approximate analytic center of C, there is a strongly polynomial-time algorithm for approximating sym(C) to any given relative tolerance. en dc.description.sponsorship Singapore-MIT Alliance (SMA) en dc.format.extent 11101 bytes dc.format.mimetype application/pdf dc.language.iso en_US dc.relation.ispartofseries High Performance Computation for Engineered Systems (HPCES); dc.subject symmetry en dc.subject geometry of convex sets en dc.subject interior-point methods en dc.title An Algorithm for Computing the Symmetry Point of a Polytope en dc.type Article en
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