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AuthorBoltyanski, V. author
TitleGeometric Methods and Optimization Problems [electronic resource] / by V. Boltyanski, H. Martini, V. Soltan
ImprintBoston, MA : Springer US : Imprint: Springer, 1999
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Descript VIII, 432 p. online resource


VII Preface In many fields of mathematics, geometry has established itself as a fruitful method and common language for describing basic phenomena and problems as well as suggesting ways of solutions. Especially in pure mathematics this is obยญ vious and well-known (examples are the much discussed interplay between linยญ ear algebra and analytical geometry and several problems in multidimensional analysis). On the other hand, many specialists from applied mathematics seem to prefer more formal analytical and numerical methods and representations. Nevertheless, very often the internal development of disciplines from applied mathematics led to geometric models, and occasionally breakthroughs were bẽd on geometric insights. An excellent example is the Klee-Minty cube, solving a problem of linear programming by transforming it into a geometยญ ric problem. Also the development of convex programming in recent decades demonstrated the power of methods that evolved within the field of convex geometry. The present book focuses on three applied disciplines: control theory, location science and computational geometry. It is our aim to demonstrate how methods and topics from convex geometry in a wider sense (separation theory of convex cones, Minkowski geometry, convex partitionings, etc.) can help to solve various problems from these disciplines

Mathematics Numerical analysis Convex geometry Discrete geometry Mathematical optimization Calculus of variations Combinatorics Mathematics Optimization Calculus of Variations and Optimal Control; Optimization Convex and Discrete Geometry Numeric Computing Combinatorics


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