Convex analysis and optimization in Hadamard spaces (Q2877477)

Convex analysis and convex optimization are usually treated in the context of vector spaces (finite dimensional or not). The present book is a systematic account of convex analysis and convex optimization in the context of Hadamard spaces. Hadamard spaces are complete geodesic spaces of nonpositive curvature. Convexity in vectors spaces is a property defined in terms of the line segment joining two points, whereas convexity in Hadamard spaces is defined in terms of the geodesics joining the two points. The overall presentation of the book is very clear and most results are illustrated with examples and applications. There are eight chapters in all, namely, 1. Geometry of nonpositive curvature; 2. Convex sets and convex functions; 3. Weak convergence in Hadamard spaces; 4. Nonexpansive mappings; 5. Gradient flow of a convex functional; 6. Convex optimization algorithms; 7. Probalistic tools in Hadamard spaces; and 8. Tree spaces and its applications.