04144nam 2200841 450 991082700500332120230803200404.03-11-036162-03-11-039108-210.1515/9783110361629(CKB)3360000000515254(EBL)1759926(SSID)ssj0001401679(PQKBManifestationID)11890656(PQKBTitleCode)TC0001401679(PQKBWorkID)11357007(PQKB)11679146(MiAaPQ)EBC1759926(DE-B1597)426521(OCoLC)1023977505(OCoLC)1029814141(OCoLC)1032688691(OCoLC)1037980950(OCoLC)1041999464(OCoLC)1043662472(OCoLC)979589493(OCoLC)987942471(OCoLC)992472044(DE-B1597)9783110361629(Au-PeEL)EBL1759926(CaPaEBR)ebr11014086(CaONFJC)MIL807204(OCoLC)898769727(EXLCZ)99336000000051525420150211h20142014 uy 0engurcnu||||||||txtccrConvex analysis and optimization in Hadamard spaces /Miroslav BačákBerlin, [Germany] ;Boston, [Massachusetts] :Walter de Gruyter GmbH,2014.©20141 online resource (194 p.)De Gruyter Series in Nonlinear Analysis and Applications,0941-813x ;Volume 22Description based upon print version of record.3-11-036103-5 Includes bibliographical references and index.Front matter --Preface --Contents --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 Probabilistic tools in Hadamard spaces --8 Tree space and its applications --References --Index --Back matterIn the past two decades, convex analysis and optimization have been developed in Hadamard spaces. This book represents a first attempt to give a systematic account on the subject. Hadamard spaces are complete geodesic spaces of nonpositive curvature. They include Hilbert spaces, Hadamard manifolds, Euclidean buildings and many other important spaces. While the role of Hadamard spaces in geometry and geometric group theory has been studied for a long time, first analytical results appeared as late as in the 1990's. Remarkably, it turns out that Hadamard spaces are appropriate for the theory of convex sets and convex functions outside of linear spaces. Since convexity underpins a large number of results in the geometry of Hadamard spaces, we believe that its systematic study is of substantial interest. Optimization methods then address various computational issues and provide us with approximation algorithms which may be useful in sciences and engineering. We present a detailed description of such an application to computational phylogenetics. The book is primarily aimed at both graduate students and researchers in analysis and optimization, but it is accessible to advanced undergraduate students as well.De Gruyter series in nonlinear analysis and applications ;Volume 22.Metric spacesG-spacesHadamard matricesConvex analysis.Convex optimization.Geodesic convexity.Hadamard space.Metric geometry.Nonpositive curvature.Metric spaces.G-spaces.Hadamard matrices.511/.6SK 870rvkBacák Miroslav1682928MiAaPQMiAaPQMiAaPQBOOK9910827005003321Convex analysis and optimization in Hadamard spaces4053358UNINA