Lectures on Variational Analysis

Asen L. Dontchev (Autor)

Buch | Hardcover

XII, 219 Seiten

2022 | 1st ed. 2021
Springer International Publishing (Verlag)
978-3-030-79910-6 (ISBN)

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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.

Preface.- Notation, Terminology and Some Functional Analysis.- Basics in Optimization.- Continuity of Set-valued Mappings.- Lipschitz Continuity of Polyhedral Mappings.- Metric Regularity.- Lyusternik-Graves Theorem.- Mappings with Convex Graphs.- Derivative Criteria for Metric Regularity.- Strong Regularity.- Variational Inequalities over Polyhedral Sets.- Nonsmooth Inverse Function Theorems.- Lipschitz Stability in Optimization.- Strong Subregularity.- Continuous Selections.- Radius of Regularity.- Newton Method for Generalized Equations.- The Constrained Linear-Quadratic Optimal Control Problem.- Regularity in Nonlinear Control.- Discrete Approximations.- Optimal Feedback Control.- Model Predictive Control.- Bibliographical Remarks and Further Reading.

"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)

Erscheinungsdatum	06.02.2022
Reihe/Serie	Applied Mathematical Sciences
Zusatzinfo	XII, 219 p. 15 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	505 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	Constrained optimization • lipschitz stability • Mathematical Programming • metric regularity • non smooth analysis • optimal control • Sensitivity • set-valued analysis • strong regularity
ISBN-10	3-030-79910-7 / 3030799107
ISBN-13	978-3-030-79910-6 / 9783030799106
Zustand	Neuware