LEADER 04144nam 2200841 450 001 9910827005003321 005 20230803200404.0 010 $a3-11-036162-0 010 $a3-11-039108-2 024 7 $a10.1515/9783110361629 035 $a(CKB)3360000000515254 035 $a(EBL)1759926 035 $a(SSID)ssj0001401679 035 $a(PQKBManifestationID)11890656 035 $a(PQKBTitleCode)TC0001401679 035 $a(PQKBWorkID)11357007 035 $a(PQKB)11679146 035 $a(MiAaPQ)EBC1759926 035 $a(DE-B1597)426521 035 $a(OCoLC)1023977505 035 $a(OCoLC)1029814141 035 $a(OCoLC)1032688691 035 $a(OCoLC)1037980950 035 $a(OCoLC)1041999464 035 $a(OCoLC)1043662472 035 $a(OCoLC)979589493 035 $a(OCoLC)987942471 035 $a(OCoLC)992472044 035 $a(DE-B1597)9783110361629 035 $a(Au-PeEL)EBL1759926 035 $a(CaPaEBR)ebr11014086 035 $a(CaONFJC)MIL807204 035 $a(OCoLC)898769727 035 $a(EXLCZ)993360000000515254 100 $a20150211h20142014 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aConvex analysis and optimization in Hadamard spaces /$fMiroslav Bac?a?k 210 1$aBerlin, [Germany] ;$aBoston, [Massachusetts] :$cWalter de Gruyter GmbH,$d2014. 210 4$dİ2014 215 $a1 online resource (194 p.) 225 1 $aDe Gruyter Series in Nonlinear Analysis and Applications,$x0941-813x ;$vVolume 22 300 $aDescription based upon print version of record. 311 $a3-11-036103-5 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tPreface --$tContents --$t1 Geometry of Nonpositive Curvature --$t2 Convex sets and convex functions --$t3 Weak convergence in Hadamard spaces --$t4 Nonexpansive mappings --$t5 Gradient flow of a convex functional --$t6 Convex optimization algorithms --$t7 Probabilistic tools in Hadamard spaces --$t8 Tree space and its applications --$tReferences --$tIndex --$tBack matter 330 $aIn the past two decades, convex analysis and optimization have been developed in Hadamard spaces. This book represents a first attempt to give a systematic account on the subject. Hadamard spaces are complete geodesic spaces of nonpositive curvature. They include Hilbert spaces, Hadamard manifolds, Euclidean buildings and many other important spaces. While the role of Hadamard spaces in geometry and geometric group theory has been studied for a long time, first analytical results appeared as late as in the 1990's. Remarkably, it turns out that Hadamard spaces are appropriate for the theory of convex sets and convex functions outside of linear spaces. Since convexity underpins a large number of results in the geometry of Hadamard spaces, we believe that its systematic study is of substantial interest. Optimization methods then address various computational issues and provide us with approximation algorithms which may be useful in sciences and engineering. We present a detailed description of such an application to computational phylogenetics. The book is primarily aimed at both graduate students and researchers in analysis and optimization, but it is accessible to advanced undergraduate students as well. 410 0$aDe Gruyter series in nonlinear analysis and applications ;$vVolume 22. 606 $aMetric spaces 606 $aG-spaces 606 $aHadamard matrices 610 $aConvex analysis. 610 $aConvex optimization. 610 $aGeodesic convexity. 610 $aHadamard space. 610 $aMetric geometry. 610 $aNonpositive curvature. 615 0$aMetric spaces. 615 0$aG-spaces. 615 0$aHadamard matrices. 676 $a511/.6 686 $aSK 870$2rvk 700 $aBaca?k$b Miroslav$01682928 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910827005003321 996 $aConvex analysis and optimization in Hadamard spaces$94053358 997 $aUNINA