Compact Textbooks in Mathematics: Around the Weierstrass Theorem

Galewski, Marek

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.

Details

Published by: Birkhäuser

Publication Date: 2024-12-21

Format: Paperback

ISBN-13: 9783031771590

DOI: 10.1007/978-3-031-77160-6

Dimensions: 235cm x155cm

Pages: 168