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The Simplest Problem in Calculus of Variations

  • Wendell Fleming
  • Raymond Rishel
Chapter
Part of the Applications of Mathematics book series (SMAP, volume 1)

Abstract

In calculus one studies the problem of minimizing f(x), where x is real or more generally x=(x1…,xn) denotes an n-tuple of real numbers. However, in many problems of interest the domain of the function to be miminized is not a portion of some finite-dimensional space V. Rather, the function is defined on some portion of an infinite-dimensional space if. We shall begin by outlining the elementary theory of minima of a function J on an abstract space V (§2).

Keywords

Optimal Control Problem Euler Equation Simple Problem Conjugate Point Internal Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1975

Authors and Affiliations

  • Wendell Fleming
    • 1
  • Raymond Rishel
    • 2
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA
  2. 2.Department of MathematicsUniversity of KentuckyLexingtonUSA

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