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|a Bacák, Miroslav,
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|a Convex analysis and optimization in Hadamard spaces /
|c Miroslav Bacák.
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|a Berlin ;
|a Boston :
|b De Gruyter,
|c [2014]
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|a 1 online resource (viii, 185 pages .)
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|a De Gruyter series in nonlinear analysis and applications ;
|v volume 22
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|a Includes bibliographical references and index.
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|a Print version record.
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|a 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.
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|a 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.
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|a <!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>
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|a In English.
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|a Metric spaces.
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|a G-spaces.
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|a Hadamard matrices.
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|a Espaces métriques.
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|a Matrices d'Hadamard.
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|a MATHEMATICS
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|a G-spaces
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|a Hadamard matrices
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|a Konvexe Analysis
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|a Hadamard-Raum
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|i Print version:
|a Bacák, Miroslav.
|t Convex analysis and optimization in Hadamard spaces.
|d Berlin ; Boston : De Gruyter, [2014]
|z 9783110361032
|z 3110361035
|w (DLC) 2014029958
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|a De Gruyter series in nonlinear analysis and applications ;
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