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EBOOK
Author Bacák, Miroslav,
Title Convex analysis and optimization in Hadamard spaces / Miroslav Bacák.
Imprint Berlin ; Boston : De Gruyter, [2014]

Author Bacák, Miroslav,
Series De Gruyter series in nonlinear analysis and applications ; volume 22
De Gruyter series in nonlinear analysis and applications ; 22.
Subject Metric spaces.
G-spaces.
Hadamard matrices.
Author Bacák, Miroslav,
Series De Gruyter series in nonlinear analysis and applications ; volume 22
De Gruyter series in nonlinear analysis and applications ; 22.
Subject Metric spaces.
G-spaces.
Hadamard matrices.
Description 1 online resource (viii, 185 pages .)
Bibliography Note Includes bibliographical references and index.
Note Print version record.
Contents 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.
Summary <!Doctype html public ""-//w3c//dtd html 4.0 transitional//en""> <html><head> <meta content=""text/html; charset=iso-8859-1"" http-equiv=content-type> <meta name=generator content=""mshtml 8.00.6001.23580""></head> <body> 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. </body></html>
Note In English.
ISBN 3110361620 (electronic bk.)
9783110361629 (electronic bk.)
3110391082
9783110391084 (electronic bk.)
9783110361032 (hardcover)
3110361035 (hardcover)
ISBN/ISSN 10.1515/9783110361629
ebc1759926
OCLC # 899328052
Additional Format Print version: Bacák, Miroslav. Convex analysis and optimization in Hadamard spaces. Berlin ; Boston : De Gruyter, [2014] 9783110361032 3110361035 (DLC) 2014029958


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