國立虎尾科技大學 |

Variational analysis of regular mappings = theory and applications /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Variational analysis of regular mappings/ by Alexander D. Ioffe.
其他題名:	theory and applications /
作者:	Ioffe, Alexander D.
出版者:	Cham :Springer International Publishing : : 2017.,
面頁冊數:	xxi, 494 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Calculus of variations. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-64277-2
ISBN:	9783319642772

Variational analysis of regular mappings = theory and applications /
Ioffe, Alexander D.

Variational analysis of regular mappingstheory and applications /[electronic resource] :by Alexander D. Ioffe. - Cham :Springer International Publishing :2017. - xxi, 494 p. :ill., digital ;24 cm. - Springer monographs in mathematics,1439-7382. - Springer monographs in mathematics..

1 The Classical Theory -- 2 Metric Theory: Phenomenology -- 3 Metric Theory: The Infinitesimal Viewpoint -- 4 Subdifferentials: A Short Introduction -- 5 Banach Space Theory: Regularity Criteria -- 6 Banach Space Theory: Special Classes of Mappings -- 7 Applications to Analysis and Optimization 1 -- 8 Regularity in Finite-Dimensional Spaces -- 9 Applications to Analysis and Optimization 2.

This monograph offers the first systematic account of (metric) regularity theory in variational analysis. It presents new developments alongside classical results and demonstrates the power of the theory through applications to various problems in analysis and optimization theory. The origins of metric regularity theory can be traced back to a series of fundamental ideas and results of nonlinear functional analysis and global analysis centered around problems of existence and stability of solutions of nonlinear equations. In variational analysis, regularity theory goes far beyond the classical setting and is also concerned with non-differentiable and multi-valued operators. The present volume explores all basic aspects of the theory, from the most general problems for mappings between metric spaces to those connected with fairly concrete and important classes of operators acting in Banach and finite dimensional spaces. Written by a leading expert in the field, the book covers new and powerful techniques, which have proven to be highly efficient even in classical settings, and outlines the theory's predominantly quantitative character, leading to a variety of new and unexpected applications. Variational Analysis of Regular Mappings is aimed at graduate students and researchers in nonlinear and functional analysis, especially those working in areas close to optimization and optimal control, and will be suitable to anyone interested in applying new concepts and ideas to operations research, control engineering and numerical analysis.

ISBN: 9783319642772

Standard No.: 10.1007/978-3-319-64277-2doiSubjects--Topical Terms:

527927
Calculus of variations.

LC Class. No.: QA315

Dewey Class. No.: 515.64

Variational analysis of regular mappings = theory and applications /
LDR:03023nam a2200349 a 4500 001 905294
003 DE-He213
005 20180426142629.0
006 m d
007 cr nn 008maaau
008 190308s2017 gw s 0 eng d
020 $a 9783319642772 $q (electronic bk.)
020 $a 9783319642765 $q (paper)
024 7 $a 10.1007/978-3-319-64277-2 $2 doi
035 $a 978-3-319-64277-2
040 $a GP $c GP
041 0 $a eng
050 4 $a QA315
072 7 $a PBKQ $2 bicssc
072 7 $a PBU $2 bicssc
072 7 $a MAT005000 $2 bisacsh
072 7 $a MAT029020 $2 bisacsh
082 0 4 $a 515.64 $2 23
090 $a QA315 $b .I64 2017
100 1 $a Ioffe, Alexander D. $3 1172349
245 1 0 $a Variational analysis of regular mappings $h [electronic resource] : $b theory and applications / $c by Alexander D. Ioffe.
260 $a Cham : $c 2017. $b Springer International Publishing : $b Imprint: Springer,
300 $a xxi, 494 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer monographs in mathematics, $x 1439-7382
505 0 $a 1 The Classical Theory -- 2 Metric Theory: Phenomenology -- 3 Metric Theory: The Infinitesimal Viewpoint -- 4 Subdifferentials: A Short Introduction -- 5 Banach Space Theory: Regularity Criteria -- 6 Banach Space Theory: Special Classes of Mappings -- 7 Applications to Analysis and Optimization 1 -- 8 Regularity in Finite-Dimensional Spaces -- 9 Applications to Analysis and Optimization 2.
520 $a This monograph offers the first systematic account of (metric) regularity theory in variational analysis. It presents new developments alongside classical results and demonstrates the power of the theory through applications to various problems in analysis and optimization theory. The origins of metric regularity theory can be traced back to a series of fundamental ideas and results of nonlinear functional analysis and global analysis centered around problems of existence and stability of solutions of nonlinear equations. In variational analysis, regularity theory goes far beyond the classical setting and is also concerned with non-differentiable and multi-valued operators. The present volume explores all basic aspects of the theory, from the most general problems for mappings between metric spaces to those connected with fairly concrete and important classes of operators acting in Banach and finite dimensional spaces. Written by a leading expert in the field, the book covers new and powerful techniques, which have proven to be highly efficient even in classical settings, and outlines the theory's predominantly quantitative character, leading to a variety of new and unexpected applications. Variational Analysis of Regular Mappings is aimed at graduate students and researchers in nonlinear and functional analysis, especially those working in areas close to optimization and optimal control, and will be suitable to anyone interested in applying new concepts and ideas to operations research, control engineering and numerical analysis.
650 0 $a Calculus of variations. $3 527927
650 0 $a Mappings (Mathematics) $3 768488
650 0 $a Differentiable mappings. $3 885647
650 1 4 $a Mathematics. $3 527692
650 2 4 $a Calculus of Variations and Optimal Control; Optimization. $3 593942
650 2 4 $a Continuous Optimization. $3 888956
650 2 4 $a Functional Analysis. $3 672166
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 672519
650 2 4 $a Difference and Functional Equations. $3 672077
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
830 0 $a Springer monographs in mathematics. $3 882184
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-64277-2
950 $a Mathematics and Statistics (Springer-11649)