02886nam a22004575i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001800172050001400190072001600204072002300220072001500243100008500258245011600343250001800459264007300477300006100550336002600611337002600637338003600663347002400699490004900723505028400772520096701056650003802023650003502061650005202096710003402148773002602182776003602208776003602244830005602280856004602336912001402382912001502396999001702411978-3-031-77160-6DE-He21320251030114630.0cr nn 008mamaa241220s2024    sz |    s    |||| 0|eng d  a97830317716069978-3-031-77160-67 a10.1007/978-3-031-77160-62doi 4aQA402.5-402.6 4aQA315-316 7aPBU2bicssc 7aMAT0420002bisacsh 7aPBU2thema1 aGalewski, Marek.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut98926210aBasics of Nonlinear Optimizationh[electronic resource] :bAround the Weierstrass Theorem /cby Marek Galewski.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Birkhäuser,c2024.  aX, 168 p. 3 illus., 1 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aCompact Textbooks in Mathematics,x2296-455X0 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.  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. 0aMathematical optimization.965522 0aCalculus of variations.96726814aCalculus of Variations and Optimization.9672702 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303177159008iPrinted edition:z9783031771613 0aCompact Textbooks in Mathematics,x2296-455X97527040uhttps://doi.org/10.1007/978-3-031-77160-6  aZDB-2-SMA  aZDB-2-SXMS  c65890d65890