Basics of Nonlinear Optimization - Galewski, Marek; - Prospero Internet Bookshop

Basics of Nonlinear Optimization: Around the Weierstrass Theorem
 
Product details:

ISBN13:9783031771590
ISBN10:3031771591
Binding:Paperback
No. of pages:168 pages
Size:235x155 mm
Language:English
Illustrations: 2 Illustrations, black & white; 1 Illustrations, color
681
Category:

Basics of Nonlinear Optimization

Around the Weierstrass Theorem
 
Edition number: 2024
Publisher: Birkhäuser
Date of Publication:
Number of Volumes: 1 pieces, Book
 
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20 420 HUF (19 448 HUF + 5% VAT)
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Short description:

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.

Long description:

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.

Table of Contents:

- 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.