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 lin- 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 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.