Basics of Nonlinear Optimization
Around the Weierstrass Theorem
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Beschreibung
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.
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.
Uses a pedagogical approach Blends theory in with exercises Allows readers to proceed smoothly to more advanced topics
Autor*in
Marek Galewski
Themen in »Basics of Nonlinear Optimization«
Weierstrass Theorem Euler Action Functional Boundary Value Problem Nonlinear Optimization Differentiation in Banach Spaces
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“This textbook is prepared with particular care to be reader-friendly. In particular, it can be perfectly used to design an advanced undergraduate or Master's course on these topics, but it can also be used as a reference book for individual study by motivated scholars in mathematics, physics or engineering. The development is progressive, accompanied by lots of remarks, examples, exercises and suggestions for further reading.” (Aris Daniilidis, Mathematical Reviews, February, 2026)
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