How to Solve Equation involving minimizer from NMinimize

Question

I am trying to solve an equation that contains the minimzer of a function. A simple example is:

x[p_] := xx /. NMinimize[(xx - p)^2, xx][[2]]
NSolve[x[p] == 0, p]

During evaluation of In[1]:= NMinimize::nnum: The function value    (-0.829053-p)^2 is not a number at {xx} = {-0.829053}. >>

During evaluation of In[1]:= NMinimize::nnum: The function value (-0.829053-p)^2 is not a number at {xx} = {-0.829053}. >>

During evaluation of In[1]:= NMinimize::nnum: The function value (-0.829053-p)^2 is not a number at {xx} = {-0.829053}. >>

During evaluation of In[1]:= General::stop: Further output of NMinimize::nnum will be suppressed during this calculation. >>

During evaluation of In[1]:= ReplaceAll::reps: {xx} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. >>

During evaluation of In[1]:= ReplaceAll::reps: {xx} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. >>

Out[2]= {}

Does anyone know how to do this? (Of course the example is trivial, the actual functions I am using are much more complicated and require NMinimize and the same error arises there.)

This one works (thanks Michael!):

x[p_?NumericQ] := xx /. NMinimize[(xx - p)^2, xx][[2]]
FindRoot[x[p], {p, 0}]

Out[7]= {p -> 0.}

Welcome to Mathematica.SE! I suggest the following: 1) As you receive help, try to give it too, by answering questions in your area of expertise. 2) Take the tour! 3) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign! — Michael E2, Aug 02 '16 at 18:23
Use x[p_?NumericQ] :=.... See http://mathematica.stackexchange.com/questions/18393/what-are-the-most-common-pitfalls-awaiting-new-users/26037#26037. — Michael E2, Aug 02 '16 at 18:24
If the actual equations are actually not algebraic, note that NSolve[] is not really meant for handling those. — J. M.'s missing motivation, Aug 02 '16 at 18:25
Also, NSolve might not be the best choice. FindRoot may work better on your actual function. — Michael E2, Aug 02 '16 at 18:25

How to Solve Equation involving minimizer from NMinimize

0 Answers0