國立虎尾科技大學 |

Lectures on Variational Analysis

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Lectures on Variational Analysis/ by Asen L. Dontchev.
作者:	Dontchev, Asen L.
面頁冊數:	XII, 219 p. 15 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Multivariate Analysis. -
電子資源:	https://doi.org/10.1007/978-3-030-79911-3
ISBN:	9783030799113

Lectures on Variational Analysis
Dontchev, Asen L.

Lectures on Variational Analysis[electronic resource] /by Asen L. Dontchev. - 1st ed. 2021. - XII, 219 p. 15 illus.online resource. - Applied Mathematical Sciences,2052196-968X ;. - Applied Mathematical Sciences,191.

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:

563891
Multivariate Analysis.

LC Class. No.: QA402.5-402.6

Dewey Class. No.: 519.6

Lectures on Variational Analysis
LDR:03121nam a22004335i 4500 001 1059879
003 DE-He213
005 20220204222127.0
007 cr nn 008mamaa
008 220414s2021 sz | s |||| 0|eng d
020 $a 9783030799113 $9 978-3-030-79911-3
024 7 $a 10.1007/978-3-030-79911-3 $2 doi
035 $a 978-3-030-79911-3
050 4 $a QA402.5-402.6
050 4 $a QA315-316
072 7 $a PBU $2 bicssc
072 7 $a MAT003000 $2 bisacsh
072 7 $a PBU $2 thema
082 0 4 $a 519.6 $2 23
082 0 4 $a 515.64 $2 23
100 1 $a Dontchev, Asen L. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 768937
245 1 0 $a Lectures on Variational Analysis $h [electronic resource] / $c by Asen L. Dontchev.
250 $a 1st ed. 2021.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a XII, 219 p. 15 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Applied Mathematical Sciences, $x 2196-968X ; $v 205
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.
650 2 4 $a Multivariate Analysis. $3 563891
650 2 4 $a Linear Algebra. $3 1207620
650 1 4 $a Calculus of Variations and Optimization. $3 1366302
650 0 $a Multivariate analysis. $3 577402
650 0 $a Algebras, Linear. $3 528115
650 0 $a Calculus of variations. $3 527927
650 0 $a Mathematical optimization. $3 527675
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030799106
776 0 8 $i Printed edition: $z 9783030799120
776 0 8 $i Printed edition: $z 9783030799137
830 0 $a Applied Mathematical Sciences, $x 0066-5452 ; $v 191 $3 1254006
856 4 0 $u https://doi.org/10.1007/978-3-030-79911-3
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)