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Re: Finding the optimum by repeteadly zooming on the solution space (or something like that)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg92575] Re: Finding the optimum by repeteadly zooming on the solution space (or something like that)
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Mon, 6 Oct 2008 04:14:14 -0400 (EDT)

On 10/5/08 at 6:05 AM, cuak2000 at gmail.com (Mauricio Esteban Cuak)
wrote:

>Hello everyone.I know somebody has probably writ mathematica code on
>this problem. A general answer would probably benefit more people,
>but I'll do the specific example, 'cause I'm not sure how to explain
>it in another way.

>I have these restrictions:

>cpoAg1= ( -x + (70*a*(x^0.4 + y^0.4)^0.75)/x^0.6);

>(*and*)

>cpoAg2= ((70*(1 - a)*(x^0.4 + y^0.4)^0.75)/y^0.6 - 2*y);

>(* And I need to find the "a" that will maximise this following
>function. I don't need and exact solution, but something that is
>sufficiently near *)

>obj =  -x^2/2 + 100*(x^0.4 + y^0.4)^1.75 - y^2;

>(* "A" goes between 0 and 1 so I discretise to obtain the {x,y} that
>maximise every "a"

>the Table command gives me the list of rules which I can replace on
>"obj" later to find the maximum. No problem here*)

>rules = Table[
>FindRoot[{cpoAg1 == 0, cpoAg2 == 0}, {{x, 0.1}, {y, 0.1}}], {a, 0.=
1,
>1, 0.1}
>];

>(*the maximum is found with this following function *)

>Max[Thread[ReplaceAll[obj, rules]]];

>So far so good...I could discretise "a" as thinly as I want, but I
>can't afford the luxury of being that inneficient, 'cause I've got
>to do other things later with this part of the program.

I don't understand why you would take this approach. Why not use
the built-in function NMaximize, That is:

In[20]:= NMaximize[{obj,
   cpoAg1 == 0 && cpoAg2 == 0 && x > 0.1 && y > 0.1}, {a, x, y}]

Out[20]= {2084.72,{a->0.527688,x->22.6727,y->13.7173}}


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