Functional Analysis, Calculus of Variations and Optimal Control

• Κύριος συγγραφέας: Clarke, Francis (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: London : Springer London : Imprint: Springer, 2013.
• Σειρά: Graduate Texts in Mathematics, 264
• Θέματα: Mathematics.; Functional analysis.; System theory.; Calculus of variations.; Mathematical optimization.; Functional Analysis.; Calculus of Variations and Optimal Control; Optimization.; Continuous Optimization.; Systems Theory, Control.

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 o...

Πίνακας περιεχομένων:

• 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
• Additional exercises for Part III
• Multiple integrals
• Necessary conditions
• Existence and regularity
• Inductive methods
• Differential inclusions
• Additional exercises for Part IV.