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130626  eng 
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a 9783540312475

100 
1 

a Mordukhovich, Boris S.

245 
0 
0 
a Variational Analysis and Generalized Differentiation I
h Elektronische Ressource
b Basic Theory
c by Boris S. Mordukhovich

250 


a 1st ed. 2006

260 


a Berlin, Heidelberg
b Springer Berlin Heidelberg
c 2006, 2006

300 


a XXII, 579 p
b online resource

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0 

a Generalized Differentiation in Banach Spaces: Generalized Normals to Nonconvex Sets. Coderivatives of SetValued Mappings. Subdifferentials of Nonsmooth Functions  Extremal Principle in Variational Analysis: Set Extremality and Nonconvex Separation. Extremal Principle in Asplund Spaces. Relations with Variational Principles. Representations and Characterizations in Asplund Spaces. Versions of the Extremal Principle in Banach Spaces  Full Calculus in Asplund Spaces: Calculus Rules for Normals and Coderivatives. Subdifferential Calculus and Related Topics. SNC Calculus for Sets and Mappings  Lipschitzian Stability and Sensivity Analysis: Neighborhood Criteria and Exact Bounds. Pointbased Characterizations. Sensitivity Analysis for Constraint Systems. Sensitivity Analysis for Variational Systems  References  Glossary of Notation  Index of Statements

653 


a Numerical Analysis

653 


a Calculus of Variations and Optimization

653 


a Numerical analysis

653 


a Manifolds (Mathematics)

653 


a Applications of Mathematics

653 


a Mathematics

653 


a Mathematical optimization

653 


a Global analysis (Mathematics)

653 


a Global Analysis and Analysis on Manifolds

653 


a Calculus of variations

041 
0 
7 
a eng
2 ISO 6392

989 


b Springer
a Springer eBooks 2005

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0 

a Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics

028 
5 
0 
a 10.1007/3540312471

856 
4 
0 
u https://doi.org/10.1007/3540312471?nosfx=y
x Verlag
3 Volltext

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0 

a 515.64

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a 519.6

520 


a Variational analysis is a fruitful area in mathematics that, on the one hand, deals with the study of optimization and equilibrium problems and, on the other hand, applies optimization, perturbation, and approximation ideas to the analysis of a broad range of problems that may not be of a variational nature. One of the most characteristic features of modern variational analysis is the intrinsic presence of nonsmoothness, which enters naturally not only through initial data of optimizationrelated problems but largely via variational principles and perturbation techniques. Thus generalized differential lies at the heart of variational analysis and its applications. This monograph in two volumes contains a comprehensive and stateofthe art study of the basic concepts and principles of variational analysis and generalized differentiation in both finitedimensional and infinite dimensional spaces and presents numerous applications to problems in the optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc. The first of volume is mainly devoted to the basic theory of variational analysis and generalized differentiations, while the second volume contains various applications. Both volumes contain abundant bibliographies and extensive commentaries. This book will be of interest to researchers and graduate students in mathematical sciences. It may also be useful to a broad range of researchers, practitioners, and graduate students involved in the study and applications of variational methods in economics, engineering, control systems, operations research, statistics, mechanics, and other applied sciences
