• To: mathgroup at smc.vnet.net
• Subject: [mg130713] Re: Minimize Headscratcher
• From: Ray Koopman <koopman at sfu.ca>
• Date: Mon, 6 May 2013 02:25:13 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• Delivered-to: l-mathgroup@wolfram.com
• Delivered-to: mathgroup-outx@smc.vnet.net
• Delivered-to: mathgroup-newsendx@smc.vnet.net

```I don't know what happened to your unconstrained solution,
but try ANDing the inequalities in the constraints.

Chop@Minimize[f, unknowns]

{54.3486, {\[Gamma] -> -199.205, \[Phi] -> 0.0000752392, \[Psi] -> 10.7476,
\[Theta][1] -> 0.563327, \[Theta][2] -> -0.074791, \[Theta][3] -> -9.96611,
\[Theta][4] -> 1.12321, \[Lambda][1] -> -2.00975, \[Lambda][2] -> -425.718}}

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

{58.8834, {\[Gamma] -> -68.0962, \[Phi] -> 0.0020316, \[Psi] -> 4.27197,
\[Theta][1] -> 0.593518, \[Theta][2] -> 0, \[Theta][3] -> 0,
\[Theta][4] -> 1.09797, \[Lambda][1] -> -2.0119, \[Lambda][2] -> -45.1056}}

\$Version
5.2 for Mac OS X (June 20, 2005)

On Sat, May 04, 2013 @ 12:18 AM, bruce colletti <bruce.colletti at gmail.com> wrote:
> 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] \
[!
>  Lambda][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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