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001 978-1-4471-4820-3
003 DE-He213
005 20140220082807.0
007 cr nn 008mamaa
008 130217s2013 xxk| s |||| 0|eng d
020 _a9781447148203
_9978-1-4471-4820-3
024 7 _a10.1007/978-1-4471-4820-3
_2doi
050 4 _aQA319-329.9
072 7 _aPBKF
_2bicssc
072 7 _aMAT037000
_2bisacsh
082 0 4 _a515.7
_223
100 1 _aClarke, Francis.
_eauthor.
245 1 0 _aFunctional Analysis, Calculus of Variations and Optimal Control
_h[electronic resource] /
_cby Francis Clarke.
264 1 _aLondon :
_bSpringer London :
_bImprint: Springer,
_c2013.
300 _aXIV, 591 p. 16 illus., 8 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v264
505 0 _aNormed Spaces -- Convex sets and functions -- Weak topologies -- Convex analysis -- Banach spaces -- Lebesgue spaces -- Hilbert spaces -- Additional exercises for Part I -- Optimization and multipliers -- Generalized gradients -- Proximal analysis -- Invariance and monotonicity -- Additional exercises for Part II -- The classical theory -- Nonsmooth extremals -- Absolutely continuous solutions -- The multiplier rule -- Nonsmooth Lagrangians -- Hamilton-Jacobi methods -- Additional exercises for Part III -- Multiple integrals -- Necessary conditions -- Existence and regularity -- Inductive methods -- Differential inclusions -- Additional exercises for Part IV.
520 _aFunctional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields.
650 0 _aMathematics.
650 0 _aFunctional analysis.
650 0 _aSystems theory.
650 0 _aMathematical optimization.
650 1 4 _aMathematics.
650 2 4 _aFunctional Analysis.
650 2 4 _aCalculus of Variations and Optimal Control; Optimization.
650 2 4 _aContinuous Optimization.
650 2 4 _aSystems Theory, Control.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781447148197
830 0 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v264
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4471-4820-3
912 _aZDB-2-SMA
999 _c94706
_d94706