Lectures on Variational Analysis

Beschreibung

This book presents an introduction to variational analysis, a field which unifies theories and techniques developed in calculus of variations, optimization, and control, and covers convex analysis, nonsmooth analysis, and set-valued analysis. It focuses on problems with constraints, the analysis of which involves set-valued mappings and functions that are not differentiable. Applications of variational analysis are interdisciplinary, ranging from financial planning to steering a flying object. The book is addressed to graduate students, researchers, and practitioners in mathematical sciences, engineering, economics, and finance. A typical reader of the book should be familiar with multivariable calculus and linear algebra. Some basic knowledge in optimization, control, and elementary functional analysis is desirable, but all necessary background material is included in the book.

This book presents an introduction to variational analysis, a field which unifies theories and techniques developed in calculus of variations, optimization, and control, and covers convex analysis, nonsmooth analysis, and set-valued analysis. It focuses on problems with constraints, the analysis of which involves set-valued mappings and functions that are not differentiable. Applications of variational analysis are interdisciplinary, ranging from financial planning to steering a flying object. The book is addressed to graduate students, researchers, and practitioners in mathematical sciences, engineering, economics, and finance. A typical reader of the book should be familiar with multivariable calculus and linear algebra. Some basic knowledge in optimization, control, and elementary functional analysis is desirable, but all necessary background material is included in the book.

Includes in-text exercises and examples Presents topics in variational analysis and optimal control to readers without a background in the field Provides overview of major developments in an evolving field with applications to finances and engineering

Autor*in

Asen L. Dontchev

Themen in »Lectures on Variational Analysis«

constrained optimization set-valued analysis non smooth analysis metric regularity strong regularity sensitivity Lipschitz stability mathematical programming optimal control

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“The book concludes with an 80-item bibliography accompanied by notes on sources of further information on the topics and theorems of each lecture. The book gives a concise, elegant introduction to fundamental concepts, techniques and theorems in variational analysis and will be helpful for both graduate students and more experienced researchers in the field.” (Doug Ward, Mathematical Reviews, May, 2023)
“This is a very nice book and can be recommended to everybody who is interested in variational analysis. All along the book, we see an effort to make accessible sometimes difficult notions and proofs, this book being a model to follow when preparing a graduate course.” (Nicolae Cîndea, zbMATH 1490.49002, 2022)
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