Functional Analysis, Calculus of Variations and Optimal 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...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Clarke, Francis (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:Inglés
Published: London : Springer London : Imprint: Springer, 2013.
Edition:1st ed. 2013.
Series:Graduate Texts in Mathematics, 264
Subjects:
Functional analysis.
Mathematical optimization.
Calculus of variations.
System theory.
Control theory.
Functional Analysis.
Calculus of Variations and Optimization.
Continuous Optimization.
Systems Theory, Control .
Online Access:Texto Completo
Table of Contents:
  • 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.

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