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Basics of nonlinear optimizationaround the Weierstrass theorem /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Basics of nonlinear optimizationby Marek Galewski.
Reminder of title:	around the Weierstrass theorem /
Author:	Galewski, Marek.
Published:	Cham :Springer Nature Switzerland :2024.
Description:	x, 168 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Functional analysis.
Online resource:	https://doi.org/10.1007/978-3-031-77160-6
ISBN:	9783031771606$q(electronic bk.)

Basics of nonlinear optimizationaround the Weierstrass theorem /
Galewski, Marek.

Basics of nonlinear optimizationaround the Weierstrass theorem /[electronic resource] :by Marek Galewski. - Cham :Springer Nature Switzerland :2024. - x, 168 p. :ill. (some col.), digital ;24 cm. - Compact textbooks in mathematics,2296-455X. - Compact textbooks in mathematics..

- 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.

ISBN: 9783031771606$q(electronic bk.)

Standard No.: 10.1007/978-3-031-77160-6doiSubjects--Topical Terms:

200585
Functional analysis.

LC Class. No.: QA320

Dewey Class. No.: 515.7

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520 $a 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.
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