Geometric Methods and Optimization Problems

by Vladimir Boltyanski, Horst Martini, V. Soltan

Overview

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 ob­ vious and well-known (examples are the much discussed interplay between linear 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 b~ed on geometric insights. An excellent example is the Klee-Minty cube, solving a problem of linear programming by transforming it into a geomet­ 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.

Product Details

ISBN-13:	9780792354543
Publisher:	Springer US
Publication date:	12/31/1998
Series:	Combinatorial Optimization , #4
Edition description:	1999
Pages:	432
Product dimensions:	6.14(w) x 9.21(h) x 0.36(d)

Table of Contents

I. Nonclassical Variational Calculus. II. Median Problems in Location Science. III. Minimum Convex Partitions of Polygonal Domains.

Editorial Reviews

Focuses on three applied disciplines: control theory, location science and computational geometry. The authors demonstrate how methods and topics from convex geometry in a wider sense, such as separation theory of convex cones, Minkowski geometry, and convex partitionings, can help solve various problems from these disciplines. They consider the tent method<-->as an application of a generalized separation theory of convex cones<-->in nonclassical variational calculus, various median problems in Euclidean and other Minkowski spaces, and different types of partitionings of topologically complicated polygonal domains into a minimum number of convex pieces. Figures and exercises are provided throughout the book. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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