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Minimize Headscratcher

  • To: mathgroup at smc.vnet.net
  • Subject: [mg130708] Minimize Headscratcher
  • From: bruce.colletti at gmail.com
  • Date: Sat, 4 May 2013 03:18:41 -0400 (EDT)
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Re 8.0.4 under Windows 7.

f is a multivariate function in the variables found in "unknowns" below.  Although not shown, f is the dot product of a vector with itself.

When I find the unconstrained minimum (over the reals) of f, Minimize returns an objective value of 902.528.

Yet when I add constraints, Minimize returns zero!

What is going on?  Thanks.

Bruce


f=4308.87\[VeryThinSpace]-2.2 \[Phi]-6.4` \[Gamma] \[Phi]-28.6` \[Gamma]^2 \[Phi]+\[Phi]^2+\[Gamma]^2 \[Phi]^2+\[Gamma]^4 \[Phi]^2-28.6` \[Psi]+2 \[Gamma]^2 \[Phi] \[Psi]+\[Psi]^2-28.6` \[Theta][1]+2 \[Gamma]^2 \[Phi] \[Theta][1]+2 \[Psi] \[Theta][1]+\[Theta][1]^2-110.8` \[Theta][2]+\[Theta][2]^2-7.4` \[Theta][3]+\[Theta][3]^2-2.2` \[Theta][4]+2 \[Phi] \[Theta][4]+\[Theta][4]^2+12.8` \[Gamma] \[Phi] \[Lambda][1]+55.2` \[Gamma]^2 \[Phi] \[Lambda][1]+55.2` \[Psi] \[Lambda][1]-110.8` \[Gamma]^2 \[Phi] \[Lambda][1]^2+\[Gamma]^2 \[Phi]^2 \[Lambda][1]^2+\[Gamma]^4 \[Phi]^2 \[Lambda][1]^2-110.8` \[Psi] \[Lambda][1]^2+2 \[Gamma]^2 \[Phi] \[Psi] \[Lambda][1]^2+\[Psi]^2 \[Lambda][1]^2+2 \[Gamma]^2 \[Phi] \[Theta][2] \[Lambda][1]^2+2 \[Psi] \[Theta][2] \[Lambda][1]^2+\[Gamma]^4 \[Phi]^2 \[Lambda][1]^4+2 \[Gamma]^2 \[Phi] \[Psi] \[Lambda][1]^4+\[Psi]^2 \[Lambda][1]^4-3.2` \[Phi] \[Lambda][2]-12.8`\[Gamma] \[Phi] \[Lambda][2]+25.6` \[Gamma] \[Phi] \[Lambda][1] \[Lambda][2]-7.4` \[Phi] \[L
 ambda][2
 ]^2+\[Phi]^2 \[Lambda][2]^2+\[Gamma]^2 \[Phi]^2 \[Lambda][2]^2+2 \[Phi] \[Theta][3] \[Lambda][2]^2+\[Gamma]^2 \[Phi]^2 \[Lambda][1]^2 \[Lambda][2]^2+\[Phi]^2 \[Lambda][2]^4;

unknowns={\[Lambda][1],\[Lambda][2],\[Gamma],\[Phi],\[Psi],\[Theta][1],\[Theta][2],\[Theta][3],\[Theta][4]};

Chop@Minimize[f,unknowns,Reals]

{902.528,{\[Lambda][1]->25.5724,\[Lambda][2]->2.0396,\[Gamma]->8.9358,\[Phi]->-0.0271413,\[Psi]->2.21744,\[Theta][1]->15.767,\[Theta][2]->21.4074,\[Theta][3]->2.26757,\[Theta][4]->1.28171}}

Chop@Minimize[{f,\[Theta][1]>=0,\[Theta][2]>=0,\[Theta][3]>=0,\[Theta][4]>=0,\[Phi]>=0,\[Psi]>=0},unknowns,Reals]

{0,{\[Lambda][1]->-2.,\[Lambda][2]->2.,\[Gamma]->4.,\[Phi]->0.8,\[Psi]->1.,\[Theta][1]->0.5,\[Theta][2]->0.200001,\[Theta][3]->0.5,\[Theta][4]->0.3}}



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