000 03804nam a22004575i 4500
001 978-1-4419-9807-1
003 DE-He213
005 20140220083730.0
007 cr nn 008mamaa
008 110623s2011 xxu| s |||| 0|eng d
020 _a9781441998071
_9978-1-4419-9807-1
024 7 _a10.1007/978-1-4419-9807-1
_2doi
050 4 _aQA440-699
072 7 _aPBM
_2bicssc
072 7 _aMAT012000
_2bisacsh
082 0 4 _a516
_223
100 1 _aKörner, Mark-Christoph.
_eauthor.
245 1 0 _aMinisum Hyperspheres
_h[electronic resource] /
_cby Mark-Christoph Körner.
264 1 _aNew York, NY :
_bSpringer New York,
_c2011.
300 _aVIII, 116 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Optimization and Its Applications,
_x1931-6828 ;
_v51
505 0 _a-Preface -- 1. Basic Concepts (Circles and Hyperspheres, Minisum Hyperspheres, Mathematical Preliminaries, Finite Dominating Sets) -- 2. Euclidean Minisum Hyperspheres (Basic Assumptions, Distance, Degenerated Solutions, Existence of Optimal Solutions, Incidence Properties, Solution Approaches for the Planar Case, Concluding Remarks) -- 3. Minisum Hyperspheres in Normed Spaces (Basic Assumptions, Distance, Degenerated Solutions, Existence of Minisum Hyperspheres, Incidence Properties, Polyhedral Norms in the Plane, Concluding Remarks) -- 4. Minisum Circle Problem with Unequal Norms (Basic Assumptions, Distance, Properties of Minisum Circles, Polyhedral Norms, Concluding Remarks) -- 5. Minisum Rectangles in a Manhattan Plane (Basic Assumptions, Notations, Point-Rectangle Distance, Restricted Problems, Unrestricted Problem, Concluding Remarks) -- 6. Extensions.– Bibliiography.– Index.
520 _aThis volume presents a self-contained introduction to the theory of minisum hyperspheres. The minisum hypersphere problem is a generalization of the famous Fermat-Torricelli problem. The problem asks for a hypersphere minimizing the weighted sum of distances to a given point set. In the general framework of finite dimensional real Banach spaces, the minisum hypersphere problem involves defining a hypersphere and calculating the distance between points and hyperspheres. The theory of minisum hyperspheres is full of interesting open problems which impinge upon the larger field of geometric optimization. This work provides an overview of the history of minisum hyperspheres as well as describes the best techniques for analyzing and solving minisum hypersphere problems. Related areas of geometric and nonlinear optimization are also discussed.  Key features of Minisum Hyperspheres include:  -assorted applications of the minisum hypersphere problem - a discussion on the existence of a solution to the problem with respect to Euclidean and other norms - several proposed extensions to the problem, including a highlight of positive and negative weights and extensive facilities extensions This work is the first book devoted to this area of research and will be of great interest to graduate students and researchers studying the minisum hypersphere problems as well as mathematicians interested in geometric optimization.
650 0 _aMathematics.
650 0 _aGeometry.
650 0 _aMathematical optimization.
650 1 4 _aMathematics.
650 2 4 _aGeometry.
650 2 4 _aOptimization.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781441998064
830 0 _aSpringer Optimization and Its Applications,
_x1931-6828 ;
_v51
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4419-9807-1
912 _aZDB-2-SMA
999 _c106131
_d106131