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Nested optimization teaser

  • To: mathgroup at
  • Subject: [mg46047] Nested optimization teaser
  • From: "Joshua A. Solomon" <J.A.Solomon at>
  • Date: Tue, 3 Feb 2004 18:20:51 -0500 (EST)
  • Sender: owner-wri-mathgroup at

Consider the toy identity function egg:

 In[1]:= egg[in_]:=NMinimize[{(x-in)^2},{{x,-1,1}}][[2,1,2]]

 In[2]:= egg[#]&/@{1,2,3}
Out[2]:= {1.,2.,3.}

Now then, clearly

 In[3]:= NMinimize[(2-a)^2,a]
Out[3]:= {0.,{a->2.}}


 In[4]:= NMinimize[(2-egg[a])^2,a]
Out[4]:= {9.,{a->0}}

I know why this happens. What I don't know, is how to properly construct a
nested optimization so this doesn't happen. Specifically, how can I find the
minimum value (and the parameter values that produce it) of a function that
depends on the minimum value of another function, which, in turn, depends on
those same parameters?

Joshua A. Solomon

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