Geometric Methods and Optimization Problems

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This work focuses on three disciplines of applied mathematics: control theory, location science and computational geometry. The author shows how methods and tools from convex geometry in a wider sense can help solve various problems from these disciplines. More precisely they consider mainly 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 (including a detailed discussion of the Fermat-Torricelli problem) and different types of partitionings of topologically complicated polygonal domains into a minimum number of convex pieces. Figures are used extensively throughout and there is also a large collection of exercises.