By Miroslav Bacak
In the prior 20 years, convex research and optimization were constructed in Hadamard areas. This ebook represents a primary try to provide a scientific account at the subject.
Hadamard areas are whole geodesic areas of nonpositive curvature. They contain Hilbert areas, Hadamard manifolds, Euclidean structures and plenty of different vital areas. whereas the position of Hadamard areas in geometry and geometric crew conception has been studied for a very long time, first analytical effects seemed as past due as within the Nineteen Nineties. Remarkably, it seems that Hadamard areas are acceptable for the idea of convex units and convex services outdoors of linear areas. on account that convexity underpins a lot of ends up in the geometry of Hadamard areas, we think that its systematic learn is of considerable curiosity. Optimization equipment then tackle a variety of computational concerns and supply us with approximation algorithms that may be invaluable in sciences and engineering. We current an in depth description of such an program to computational phylogenetics.
The ebook is essentially geared toward either graduate scholars and researchers in research and optimization, however it is available to complex undergraduate scholars as well.
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Convex analysis and optimization in Hadamard spaces (De Gruyter Series in Nonlinear Analysis and Applications) by Miroslav Bacak