The Weierstrass Necessary Condition

  • George Leitmann
Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG, volume 24)


We return now to a consideration of further necessary conditions for a minimizing function x*(·) of the integral J(·). Thus far we have shown the necessity of the Euler condition in its various forms; we recall that it is a necessary condition for both a weak local, and hence a strong local as well as a global minimum and maximum of J(·). Now we shall deduce a condition, the Weierstrass condition, that is necessary for a strong local, and hence a global minimum of J(·); it is not necessary for a weak local minimum.


Local Minimum Local Maximum Global Minimum Discontinuity Point Excess Function 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1981

Authors and Affiliations

  • George Leitmann
    • 1
  1. 1.University of CaliforniaBerkeleyUSA

Personalised recommendations