LEADER 02851nam 22005295 450 001 9910918600903321 005 20251107172728.0 010 $a9783031771606 010 $a3031771605 024 7 $a10.1007/978-3-031-77160-6 035 $a(MiAaPQ)EBC31854757 035 $a(Au-PeEL)EBL31854757 035 $a(CKB)37058961000041 035 $a(DE-He213)978-3-031-77160-6 035 $a(EXLCZ)9937058961000041 100 $a20241220d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aBasics of Nonlinear Optimization $eAround the Weierstrass Theorem /$fby Marek Galewski 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Birkhäuser,$d2024. 215 $a1 online resource (173 pages) 225 1 $aCompact Textbooks in Mathematics,$x2296-455X 311 08$a9783031771590 311 08$a3031771591 327 $a- 1. The Weierstrass Theorem - the origin of optimization -- 2. Some basics from functional analysis and function spaces -- 3. Differentiation in infinite dimensional spaces -- 4. On the Weierstrass Theorem in infinite dimensional spaces -- 5. Applications to multiple integrals. 330 $aThis textbook gives an introduction to optimization tools which arise around the Weierstrass theorem about the minimum of a lower semicontinuous function. Starting from a Euclidean space, it moves further into the infinite dimensional setting towards the direct variational method, going through differentiation and introducing relevant background information on the way. Exercises accompany the text and include observations, remarks, and examples that help understand the presented material. Although some basic knowledge of functional analysis is assumed, covering Hilbert and Banach spaces and the Lebesgue integration, the required background material is covered throughout the text, and literature suggestions are provided. For less experienced readers, a summary of some optimization techniques is also included. The book will appeal to both students and instructors in specialized courses on optimization, wishing to learn more about variational methods. 410 0$aCompact Textbooks in Mathematics,$x2296-455X 606 $aMathematical optimization 606 $aCalculus of variations 606 $aCalculus of Variations and Optimization 615 0$aMathematical optimization. 615 0$aCalculus of variations. 615 14$aCalculus of Variations and Optimization. 676 $a519.6 676 $a515.64 700 $aGalewski$b Marek$01069540 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910918600903321 996 $aBasics of Nonlinear Optimization$94305907 997 $aUNINA LEADER 01980oas 2200733 a 450 001 9910895382703321 005 20251105213014.0 035 $a(DE-599)ZDB2560557-4 035 $a(OCoLC)259367685 035 $a(CONSER) 2009263070 035 $a(CKB)1000000000375730 035 $a(EXLCZ)991000000000375730 100 $a20080930b20072014 sy 101 0 $aeng 135 $aurun||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 04$aThe open endocrinology journal 210 $a[Hilversum] $c[Bentham Science Publishers]$d[2007]-[2014] 215 $a1 online resource (7 volumes) 300 $aRefereed/Peer-reviewed 311 08$a1874-2165 517 1 $aTOEJ 606 $aEndocrinology$vPeriodicals 606 $aEndocrine glands$xDiseases$vPeriodicals 606 $aEndocrinology 606 $aEndocrinology 606 $aEndocrinologie$vPe?riodiques 606 $aGlandes endocrines$xMaladies$vPe?riodiques 606 $aEndocrinologie 606 $aEndocrine glands$xDiseases$2fast$3(OCoLC)fst00909726 606 $aEndocrinology$2fast$3(OCoLC)fst00909749 608 $aPeriodicals.$2fast 615 0$aEndocrinology 615 0$aEndocrine glands$xDiseases 615 0$aEndocrinology. 615 12$aEndocrinology. 615 6$aEndocrinologie 615 6$aGlandes endocrines$xMaladies 615 6$aEndocrinologie. 615 7$aEndocrine glands$xDiseases. 615 7$aEndocrinology. 801 0$bOCLCS 801 1$bOCLCS 801 2$bOCLCS 801 2$bTXA 801 2$bHEBIS 801 2$bOCLCQ 801 2$bCUS 801 2$bOCLCQ 801 2$bOCLCF 801 2$bOCLCO 801 2$bOCLCQ 801 2$bVT2 801 2$bOCLCQ 801 2$bCASUM 801 2$bOCLCO 801 2$bCUS 801 2$bOCLCQ 906 $aJOURNAL 912 $a9910895382703321 996 $aThe open endocrinology journal$94271661 997 $aUNINA