非線形最適化の基礎（テキスト） Basics of Nonlinear Optimization : Around the Weierstrass Theorem (Compact Textbooks in Mathematics) （2024）

Galewski, Marek

Birkhauser Verlag AG（2024/12発売）

Birkhauser Verlag AG（2024/12発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 168 p.
• 商品コード 9783031771590

Full 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.

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.