Nested optimization teaser

*To*: mathgroup at smc.vnet.net*Subject*: [mg46047] Nested optimization teaser*From*: "Joshua A. Solomon" <J.A.Solomon at city.ac.uk>*Date*: Tue, 3 Feb 2004 18:20:51 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

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.}} However, 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? js -- Joshua A. Solomon http://www.staff.city.ac.uk/~solomon