VII Preface in lots of fields of arithmetic, geometry has verified itself as a fruitful procedure and customary language for describing easy phenomena and difficulties in addition to suggesting methods of suggestions. specially in natural arithmetic this can be ob­ vious and recognized (examples are the a lot mentioned interaction among lin­ ear algebra and analytical geometry and a number of other difficulties in multidimensional analysis). nevertheless, many experts from utilized arithmetic appear to want extra formal analytical and numerical tools and representations. however, quite often the inner improvement of disciplines from utilized arithmetic ended in geometric types, and infrequently breakthroughs have been b~ed on geometric insights. an exceptional instance is the Klee-Minty dice, fixing an issue of linear programming via reworking it right into a geomet­ ric challenge. additionally the improvement of convex programming in contemporary many years confirmed the facility of equipment that developed in the box of convex geometry. the current publication makes a speciality of 3 utilized disciplines: regulate concept, place technology and computational geometry. it really is our goal to illustrate how equipment and subject matters from convex geometry in a much wider feel (separation concept of convex cones, Minkowski geometry, convex partitionings, etc.) may help to resolve a variety of difficulties from those disciplines.

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