LEADER 03334nam 22005535 450 001 9911020420803321 005 20260223151150.0 010 $a3-031-92477-0 024 7 $a10.1007/978-3-031-92477-4 035 $a(MiAaPQ)EBC32259775 035 $a(Au-PeEL)EBL32259775 035 $a(CKB)40246934200041 035 $a(DE-He213)978-3-031-92477-4 035 $a(EXLCZ)9940246934200041 100 $a20250811d2025 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aOn Range Space Techniques, Convex Cones, Polyhedra and Optimization in Infinite Dimensions /$fby Paolo d'Alessandro 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (726 pages) 311 08$a3-031-92476-2 327 $a-- Introduction. -- Basic Facts of Set Theory. -- Linear Spaces. -- Rudiments of General Topology. -- Filters: the Fifth Equivalence. -- Hahn Banach andSeparation Theorems. -- Locally Convex and Barrelled Spaces. -- Metrics and pseudometrics, Norms and Pseudonorms. -- Topological Form of Hahn Banach and Separation Theorems. -- Extreme points, Faces, Support and the KreinMilman Theorem. -- Function Spaces. 330 $aThis book is a research monograph with specialized mathematical preliminaries. It presents an original range space and conic theory of infinite dimensional polyhedra (closed convex sets) and optimization over polyhedra in separable Hilbert spaces, providing, in infinite dimensions, a continuation of the author's book: A Conical Approach to Linear Programming, Scalar and Vector Optimization Problems, Gordon and Breach Science Publishers, Amsterdam, 1997. It expands and improves author's new approach to the Maximum Priciple for norm oprimal control of PDE, based on theory of convex cones, providing shaper results in various Hilbert space and Banach space settings. It provides a theory for convex hypersurfaces in lts and Hilbert spaces. For these purposes, it introduces new results and concepts, like the generalizations to the non compact case of cone capping and of the Krein Milman Theorem, an extended theory of closure of pointed cones, the notion of beacon points, and a necessary and sufficient condition of support for void interior closed convex set (complementing the Bishop Phelps Theorem), based on a new decomposition of non closed non pointed cones with non closed lineality space. 606 $aMathematical optimization 606 $aContinuous Optimization 606 $aOptimization 606 $aOptimitzaciķ matemātica$2thub 606 $aPoliedres$2thub 606 $aProgramaciķ lineal$2thub 608 $aLlibres electrōnics$2thub 615 0$aMathematical optimization. 615 14$aContinuous Optimization. 615 24$aOptimization. 615 7$aOptimitzaciķ matemātica 615 7$aPoliedres 615 7$aProgramaciķ lineal 676 $a519.6 700 $aD'Alessandro$b Paolo$017834 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911020420803321 996 $aOn Range Space Techniques, Convex Cones, Polyhedra and Optimization in Infinite Dimensions$94420245 997 $aUNINA