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MathGroup Archive 2005

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Re: Mathematica hangs when solving sys. of equations w/ certain parameters

  • To: mathgroup at smc.vnet.net
  • Subject: [mg55611] Re: [mg55586] Mathematica hangs when solving sys. of equations w/ certain parameters
  • From: "Janos D. Pinter" <jdpinter at hfx.eastlink.ca>
  • Date: Thu, 31 Mar 2005 01:24:04 -0500 (EST)
  • References: <200503300821.DAA21889@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Sean,

is your objective to find analytical expressions for all local optima, or 
you want to find best (global) solutions for certain parameters? The first 
task could be elusive; for the second you could try to use NMinimize or 
MathOptimizer.

Regards,

Janos D. Pinter, PhD, DSc
PCS Inc.
E-mail: jdpinter at hfx.eastlink.ca
Web: www.pinterconsulting.com





At 04:21 AM 3/30/2005, Sean wrote:

>I am trying to find local maxima of an objective function by solving the 
>FOCs of a function of 4 control variables (pL,pH,phiL,phiH) and 3 
>parameters (c, pDBS,phiDBS).
>
>The objective function is
>
>f[pL_,phiL_,pH_,phiH_,pDBS_,phiDBS_,c_] = \
>(pL-0.5c*phiL^2)*((pH-pL)/(phiH-phiL) - pL/phiL) + \
>(pH-0.5c*phiH^2)*((pDBS-pH)/(phiDBS-phiH) - (pH-pL)/(phiH-phiL))
>
>I find the FOCs by differentiating with respect to each of the 4 control 
>variables, and then I solve the system using Solve[] (see details below)
>
>For certain values of the parameters (c, pDBS, phiDBS), the Solve[] 
>routine works fine. But I can't figure out why Solve[] just seems to hang 
>for other parameter values. I have verified that it's not because I'm 
>dividing by zero or anything, and the points that are causing problems 
>seem to be totally generic.
>
>For example, everything works fine when (c=0.1, pDBS=5, phiDBS=8) and when 
>(c=0.1, pDBS=7, phiDBS=8), but not when (c=0.1, pDBS=6, phiDBS=8). I 
>happen to know that at these latter parameter values, one of the solutions 
>to the system is (pL=11.25, pH=0, phiL=15, phiH=0), and when I manually 
>plug this solution into the FOCs, everything evaluates to zero as 
>expected. I have also verified that I am not dividing anything by zero at 
>this solution.
>
>I was wondering whether anybody else has ever experienced problems with 
>Solve[] working for some parameter values but not for others, when there 
>should be no obvious reason why it wouldn't work.
>
>Thanks for your help! I'm new to this forum, and did a search to make sure 
>that this question hasn't been asked previously, but didn't see anything 
>of this nature.
>
>---------------------------------------------
>Details
>---------------------------------------------
>focpL[pL_,phiL_,pH_,phiH_,pDBS_,phiDBS_,c_] = 
>D[f[pL,phiL,pH,phiH,pDBS,phiDBS,c],pL]
>focphiL[pL_,phiL_,pH_,phiH_,pDBS_,phiDBS_,c_] = 
>D[f[pL,phiL,pH,phiH,pDBS,phiDBS,c],phiL]
>focpH[pL_,phiL_,pH_,phiH_,pDBS_,phiDBS_,c_] = 
>D[f[pL,phiL,pH,phiH,pDBS,phiDBS,c],pH]
>focphiH[pL_,phiL_,pH_,phiH_,pDBS_,phiDBS_,c_] = 
>D[f[pL,phiL,pH,phiH,pDBS,phiDBS,c],phiH]
>
>pDBS:= 6.0
>phiDBS:= 8
>c:=0.1
>
>solution = \ Solve[{focpL[pL,phiL,pH,phiH,pDBS,phiDBS,c]==0, \
>focphiL[pL,phiL,pH,phiH,pDBS,phiDBS,c]==0, \
>focpH[pL,phiL,pH,phiH,pDBS,phiDBS,c]==0, \
>focphiH[pL,phiL,pH,phiH,pDBS,phiDBS,c]==0},{pL,phiL,pH,phiH}]
>
>
>
>
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