Basics of Nonlinear Optimization: Around the Weierstrass Theorem 2024th Edition

“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)

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.