Miroslav Bačák, Convex analysis and optimization in Hadamard spaces, De Gruyter Series in Nonlinear Analysis and Applications, Vol. 22, viii + 185 pp, Walter de Gruyter, Berlin, 2014, ISBN 978-3-11-036103-2/hbk; 978-3-11-036162-9/ebook.

Abstract

In recent years, concepts and traditional results from convex analysis have been extended to nonlinear settings. Due to their rich geometry, CAT(0) spaces (also known as spaces of non-positive curvature in the sense of Alexandrov) proved to be relevant in this context. The aim of this book is to present a systematic discussion of various topics in convex analysis in the setting of Hadamard spaces (that is, complete CAT(0) spaces). The book contains eight chapters which combine techniques from analysis, geometry, probability and optimization to study different problems in convex analysis.