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Basics of nonlinear optimization = around the Weierstrass theorem /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Basics of nonlinear optimization/ by 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.
[NT 15003449]:	- 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.
Contained By:	Springer Nature eBook
Subject:	Functional analysis. -
Online resource:	https://doi.org/10.1007/978-3-031-77160-6
ISBN:	9783031771606

Basics of nonlinear optimization = around 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

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

531838
Functional analysis.

LC Class. No.: QA320

Dewey Class. No.: 515.7

Basics of nonlinear optimization = around the Weierstrass theorem /
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490 1 $a Compact textbooks in mathematics, $x 2296-455X
505 0 $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.
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.
650 0 $a Functional analysis. $3 531838
650 0 $a Mathematical optimization. $3 517763
650 0 $a Nonlinear theories. $3 524352
650 1 4 $a Calculus of Variations and Optimization. $3 3538813
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950 $a Mathematics and Statistics (SpringerNature-11649)