TY - BOOK AU - Bacák,Miroslav TI - Convex analysis and optimization in Hadamard spaces T2 - De Gruyter series in nonlinear analysis and applications SN - 3110361620 AV - QA611.28 .B33 2014 U1 - 511/.6 23 PY - 2014///] CY - Berlin, Boston PB - De Gruyter KW - Metric spaces KW - G-spaces KW - Hadamard matrices KW - Espaces métriques KW - Matrices d'Hadamard KW - MATHEMATICS KW - General KW - bisacsh KW - fast KW - Konvexe Analysis KW - gnd KW - Konvexe Optimierung KW - Hadamard-Raum KW - Electronic books N1 - Includes bibliographical references and index; Preface; 1 Geometry of nonpositive curvature; 1.1 Geodesic metric spaces; 1.2 Meet Hadamard spaces; 1.3 Equivalent conditions for CAT(0); 2 Convex sets and convex functions; 2.1 Convex sets; 2.2 Convex functions; 2.3 Convexity and probability measures; 3 Weak convergence in Hadamard spaces; 3.1 Existence of weak limits; 3.2 Weak convergence and convexity; 3.3 An application in fixed point theory; 4 Nonexpansive mappings; 4.1 Kirszbraun-Valentine extension; 4.2 Resolvent of a nonexpansive mapping; 4.3 Strongly continuous semigroup; 5 Gradient flow of a convex functional; 5.1 Gradient flow semigroup5.2 Mosco convergence and its consequences; 5.3 Lie-Trotter-Kato formula; 6 Convex optimization algorithms; 6.1 Convex feasibility problems; 6.2 Fixed point approximations; 6.3 Proximal point algorithm; 7 Probabilistic tools in Hadamard spaces; 7.1 Random variables and expectations; 7.2 Law of large numbers; 7.3 Conditional expectations; 8 Tree space and its applications; 8.1 Construction of the BHV tree space; 8.2 Owen-Provan algorithm; 8.3 Medians and means of trees; References; Index N2 - This book gives a first systematic account on the subject of convex analysis and optimization in Hadamard spaces. It is primarily aimed at both graduate students and researchers in analysis and optimization. UR - https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=887035 ER -