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MathGroup Archive 1997

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It's me again

  • To: mathgroup at smc.vnet.net
  • Subject: [mg7799] It's me again
  • From: Chen-Ying Huang <huang3 at fas.harvard.edu>
  • Date: Tue, 8 Jul 1997 22:41:12 -0400
  • Organization: Department of Economics
  • Sender: owner-wri-mathgroup at wolfram.com

Hi:
  I sent the message entitled "a quick question" couple of minutes ago.
In fact, my question is a little bit more complicated than that. My
ultimate goal is to write a program of "cobweb algorithm"(Is this
algorithm available anywhere?). The reason why I need this algorithm is
because I have 3 functions and there are 6 variables in each functions.
Let's call the functions F1,F2,F3, and variables a1,b1,a2,b2,a3,b3. What
I want to do is that imagine person 1's goal is to maximize F1 and he
has control over a1,b1. Similary, person 2,3 want to maximize F2, F3 and
they have control over {a2,b2},{a3,b3} respectively. Calculus tells us
that now in order to solve this question, we will have 6 simlutaneous
equations (or 6 first order conditions) to solve. But since my F1,F2, F3
are extremely complicated, the computer has been running like 24 hours
and then suddenly crashed because out of memory. So, I was just thinking
to do the following. First of all, temporarily set {b1,a2,b2,a3,b3} all
to be zero and then maximize F1 with respect to {a1}. Now given this
optimal {a1}, and temporarily set {a2,b2,a3,b3} to be zero then maximize
F1 with respect to {b1}. Continue in this way (one variable for one
time)to do maximization for each variable until that no one, given his
turn, will no longer want to change his control variable of either a or
b. This algorithm (cobweb) should run faster if I can do it since it is
only single variable optimization. So, in order to do this, I need to be
able first restore the optimal value for FindMinimum somewhere and then
continously change it until I get a fixed point. Can someone give me a
help on this matter? It is quite urgent! Thank you so much in advance.
Chen-Ying Huang


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