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I am curios to know whether there is anyway to be sure that we found all the stationary points using Lagrange multiplier method.? Thank you.

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    $\begingroup$ By being careful not to drop any solutions on the way? $\endgroup$ Nov 11, 2018 at 13:53
  • $\begingroup$ not so sure always. $\endgroup$
    – sam soft
    Nov 11, 2018 at 13:54
  • $\begingroup$ Your title and your question seem to be about two different things. Are you asking how can you be sure that you find all the maximizers and/or minimizers using the Lagrange multiplier mehtod, or are you asking how can you be sure you found all the stationary points of the Lagrangean? (These are different questions because the maximizer and/or minimizer may not be stationary points of the Lagrangean.) $\endgroup$
    – smcc
    Nov 11, 2018 at 15:21
  • $\begingroup$ Do you have a specific example in mind? $\endgroup$
    – saulspatz
    Nov 11, 2018 at 15:22
  • $\begingroup$ @smcc Yes i meant the same $\endgroup$
    – sam soft
    Nov 11, 2018 at 15:23

1 Answer 1

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Following the procedure going, without any guessing involved, and not dropping any solutions on the way(for example, +- issue) one can be sure, that there were no stationary points left out. You can be sure in that, for example, if you look at the derivation of Euler-Lagrange theorem.

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