Functional analysis, calculus of variations and optimal control
Clarke, Francis
1948-
creator
text
bibliography
enk
London
New York
Springer
c2013
2013
monographic
eng
xiv, 591 p. : ill. (some col.) ; 24 cm.
"Functional 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"--P. [4] of cover.
Normed 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 -- Multiple integrals -- Additional exercises for Part III -- Necessary conditions -- Existence and regularity -- Inductive methods -- Differential inclusions -- Additional exercises for Part IV.
Francis Clarke.
Includes bibliographical references (p. 583-584) and index.
Functional analysis
Calculus of variations
Mathematical optimization
Control theory
515.7 CLA
Graduate texts in mathematics ; 264
9781447148197 (alk. paper)
1447148193 (alk. paper)
2013931980
BTCTA
130130
20170404163346.0
17607396
eng