Lectures on Variational Analysis

AvAsen L. Dontchev

Häftad, Engelska, 2023

Del 205 i serien Applied Mathematical Sciences

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2023-02-05
Mått:155 x 235 x 13 mm
Vikt:359 g
Format:Häftad
Språk:Engelska
Serie:Applied Mathematical Sciences
Antal sidor:219
Förlag:Springer Nature Switzerland AG
ISBN:9783030799137

Utforska kategorier

Optimering inom Naturvetenskap och teknik
Matematisk statistik inom Naturvetenskap och teknik
Algebra inom Naturvetenskap och teknik

Recensioner i media

“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)

Innehållsförteckning

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.