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Geometric Methods and Optimization Problems (Hardcover, 1999 ed.)
Loot Price: R7,801
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Geometric Methods and Optimization Problems (Hardcover, 1999 ed.)
Series: Combinatorial Optimization, 4
Expected to ship within 10 - 15 working days
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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."
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