help-glpk
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## Re: [Help-glpk] minimising after maximising

 From: Michael Hennebry Subject: Re: [Help-glpk] minimising after maximising Date: Mon, 6 Jun 2011 10:16:20 -0500 (CDT) User-agent: Alpine 1.00 (DEB 882 2007-12-20)

```On Mon, 6 Jun 2011, Nick Farrell wrote:

```
```Wouldn't that mean that z[] was always >= 3?
```
```
Yes.  That is what you asked for.

```
```I want z[j] to be x[j] if x[j] < 3, 3 otherwise.
```
```
Minimizing a minimum is trickier.

z[j] <= x[j]
z[j] <= 3
z[j] >= 3 - M[j] b[j]
z[j] >= x[j] - N[j] (1-b[j])

where the b's are new binary variables and the
M's and N's are new, possibly large, constants.

Selecting their values is left as an exercise for the reader.

```
```On Mon, Jun 6, 2011 at 11:24 AM, Michael Hennebry <

```
```On Sun, 5 Jun 2011, Nick Farrell wrote:

I'm pretty new to linear programming and would like a quick tip.
```
```
In the script below, what I *want* to happen is that I first choose the
worst (ie: max) of x[p] and 3, and then solve for the minimum sum of these
values.

```
```
z[j]>=x[j]
z[j]>=3

ie: I would like z to look like: {1, 2, 3, 3, 3} and then to minimise on
```
```the
sum of these.

```
```
min SUM z[j]
j
```
```
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