000 04995nam a22005895i 4500
001 978-3-540-31246-8
003 DE-He213
005 20161121231032.0
007 cr nn 008mamaa
008 100301s2006 gw | s |||| 0|eng d
020 _a9783540312468
_9978-3-540-31246-8
024 7 _a10.1007/3-540-31246-3
_2doi
050 4 _aQA315-316
050 4 _aQA402.3
050 4 _aQA402.5-QA402.6
072 7 _aPBKQ
_2bicssc
072 7 _aPBU
_2bicssc
072 7 _aMAT005000
_2bisacsh
072 7 _aMAT029020
_2bisacsh
082 0 4 _a515.64
_223
100 1 _aMordukhovich, Boris S.
_eauthor.
245 1 0 _aVariational Analysis and Generalized Differentiation II
_h[electronic resource] :
_bApplications /
_cby Boris S. Mordukhovich.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2006.
300 _aXXII, 610 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
_x0072-7830 ;
_v331
505 0 _aConstrained Optimization and Equilibria: Necessary Optimality Conditions in Nondifferentiable Programming. Mathematical Programs with Equilibrium Constraints. Multiobjective Optimization. Subextremality and Suboptimality at Linear Rate -- Optimal Control of Evolution Systems in Banach Spaces: Optimal Control of Discrete-Time and Continuous-time Evolution Inclusions. Necessary Optimality Conditions for Differential Inclusions without Relaxation. Maximum Principle for Continuous-Time Systems with Smooth Dynamics. Approximate Maximum Principle in Optimal Control -- Optimal Control of Distributed Systems: Optimization of Differential-Algebraic Inclusions with Delays. Neumann Boundary Control of Semilinear Constrained Hyperbolic Equations. Drichelet Boundary Control of Linear Constrained Hyperbolic Equations. Minimax Control of Parabolic Systems with Pointwise State Constraints -- Applications to Economics: Models of Welfare Economics. Second Welfare Theorem for Nonconvex Economics. Nonconvex Economics with Ordered Commodity Spaces. Further Extensions and Public Goods -- References -- Glossary of Notation -- Index of Statements.
520 _aVariational analysis has been recognized as 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 natur. One of the most characteristic features of modern variational analysis is the intrinsic presence of nonsmoothness, which naturally enters not only through initial data of optimization-related problems but largely via variational principles and perturbation techniques. Thus generalized differential lies at the hear of variational analysis and its applications. This monographs contains a comprehensive and and state-of-the art study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite dimensional spaces and presents numerous applications to problems in the optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc. The book is published in two volumes, the first of which 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.
650 0 _aMathematics.
650 0 _aGlobal analysis (Mathematics).
650 0 _aManifolds (Mathematics).
650 0 _aApplied mathematics.
650 0 _aEngineering mathematics.
650 0 _aNumerical analysis.
650 0 _aCalculus of variations.
650 1 4 _aMathematics.
650 2 4 _aCalculus of Variations and Optimal Control; Optimization.
650 2 4 _aMathematics, general.
650 2 4 _aGlobal Analysis and Analysis on Manifolds.
650 2 4 _aNumerical Analysis.
650 2 4 _aApplications of Mathematics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540254386
830 0 _aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
_x0072-7830 ;
_v331
856 4 0 _uhttp://dx.doi.org/10.1007/3-540-31246-3
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c507592
_d507592