# The Simplest Problem in Calculus of Variations

Chapter

## Abstract

In calculus one studies the problem of minimizing *f(x*), where *x* is real or more generally *x*=(*x*_{1}…,*x*_{n}) 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
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## Copyright information

© Springer-Verlag New York Inc. 1975