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Lectures on variational analysis

Dontchev, A. L.

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Lectures on variational analysis

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Lectures on variational analysis/ by Asen L. Dontchev.
作者:	Dontchev, A. L.
出版者:	Cham :Springer International Publishing : : 2021.,
面頁冊數:	1 online resource (xii, 219 p.) :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Mathematical analysis. -
電子資源:	https://doi.org/10.1007/978-3-030-79911-3
ISBN:	9783030799113

Lectures on variational analysis
Dontchev, A. L.

Lectures on variational analysis[electronic resource] /by Asen L. Dontchev. - Cham :Springer International Publishing :2021. - 1 online resource (xii, 219 p.) :ill., digital ;24 cm. - Applied mathematical sciences,v. 2052196-968X ;. - Applied mathematical sciences ;v. 205..

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.

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.

ISBN: 9783030799113

Standard No.: 10.1007/978-3-030-79911-3doiSubjects--Topical Terms:

516833
Mathematical analysis.

LC Class. No.: QA300 / D66 2021

Dewey Class. No.: 515

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505 0 $a 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.
520 $a 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.
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650 0 $a Control theory. $3 535880
650 1 4 $a Calculus of Variations and Optimization. $3 3538813
650 2 4 $a Linear Algebra. $3 3338825
650 2 4 $a Multivariate Analysis. $3 788400
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950 $a Mathematics and Statistics (SpringerNature-11649)