       ConstrainedMin and vector-notation

• To: mathgroup at smc.vnet.net
• Subject: [mg21585] ConstrainedMin and vector-notation
• From: nielsx at bigfoot.com
• Date: Sat, 15 Jan 2000 02:04:28 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```I have the following problem: (used to calculate the Farell efficiency
measure, for those interested)

min l

s.t.

t(X) z <= l y
zi >= 0
z1 + ... + zn = 1

X: matrix, z, y: vectors, l: scalar
(t(X) is the matrix X transposed)

I want to solve this with ConstrainedMin. (I realize it can be rewritten on
matrixform and fed to LinearProgramming.)

The following works fine, but I wonder, if it's not possible to write it in
an easier way:

X = {{1, 3}, {7, 1}}
y = {8, 4}

n = Length[X];
zz = Table[z[i], {i, n}];
ConstrainedMin[l,
Table[z[i] >= 0, {i, n}], {Plus @@ zz == 1}], Append[zz, l]]

The point is of course, that is has to work with

X = {{3, 6}, {4, 4}, {8, 2}}

too, and an y-vector of a higher dimension for that matter.

Can anyone help me write this more elegantly??

I often encounter situation where I have to define a vector like zz to obtain
a vector-solution (e.g. when using Solve). There has to be a simpler way.

Regards,

Niels Elken Sønderby
nielsx at bigfoot.com

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