03127nam a22005175i 4500 978-3-031-77160-6 DE-He213 20251030114630.0 cr nn 008mamaa 241220s2024 sz | s |||| 0|eng d 9783031771606 978-3-031-77160-6 10.1007/978-3-031-77160-6 doi QA402.5-402.6 QA315-316 PBU bicssc MAT042000 bisacsh PBU thema Galewski, Marek. author. aut http://id.loc.gov/vocabulary/relators/aut 89262 Basics of Nonlinear Optimization [electronic resource] : Around the Weierstrass Theorem / by Marek Galewski. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2024. X, 168 p. 3 illus., 1 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Compact Textbooks in Mathematics, 2296-455X - 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. This 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. Mathematical optimization. 65522 Calculus of variations. 67268 Calculus of Variations and Optimization. 67270 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031771590 Printed edition: 9783031771613 Compact Textbooks in Mathematics, 2296-455X 75270 https://doi.org/10.1007/978-3-031-77160-6 ZDB-2-SMA ZDB-2-SXMS 65890 65890