Basic Concepts

  • Henning Tolle
Part of the Universitext book series (UTX)


The simplest optimization problem is concerned with the determination of the values of independent variables which maximize or minimize a given function of these variables. That is, in the simplest case we have to determine the values of t for which
$$ i = l(t) = \left\{ {\begin{array}{*{20}{l}} {\max .} \\ {or\min .} \end{array}} \right. $$
holds. The problem next in complexity is to find the derivatives of functions of variables which allow the integral of a function of functions of variables and their derivatives to assume an extremal value. The simplest requirement here is: Find the values of y′(t) for which
$$ J = \int\limits_{{t_A}}^{{t_E}} L [t,y(t),{y^1}(t)]dt = \left\{ {\begin{array}{*{20}{c}} {\max .} \\ {or\min .} \end{array}} \right.withy({t_A}) = A;y({t_E}) = E $$
is satisfied.


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Copyright information

© Springer-Verlag New York Inc. 1975

Authors and Affiliations

  • Henning Tolle
    • 1
  1. 1.Fachgebiet RegelsystemstheorieTechnische Hochschule Darmstadt61 DarmstadtWest Germany

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