The Simplest Problem in Calculus of Variations

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


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).


Optimal Control Problem Euler Equation Simple Problem Conjugate Point Internal Point 
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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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