By Miroslav Bacak
In the prior twenty years, convex research and optimization were built in Hadamard areas. This booklet represents a primary try to supply a scientific account at the subject.
Hadamard areas are whole geodesic areas of nonpositive curvature. They comprise Hilbert areas, Hadamard manifolds, Euclidean constructions and lots of different vital areas. whereas the function of Hadamard areas in geometry and geometric crew thought has been studied for a very long time, first analytical effects seemed as overdue as within the Nineteen Nineties. Remarkably, it seems that Hadamard areas are acceptable for the speculation of convex units and convex services open air of linear areas. given that convexity underpins plenty of leads to the geometry of Hadamard areas, we think that its systematic examine is of considerable curiosity. Optimization tools then deal with a variety of computational concerns and supply us with approximation algorithms that could be worthwhile in sciences and engineering. We current an in depth description of such an software to computational phylogenetics.
The booklet is essentially aimed 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