Re: ConstrainedMin with negative variables

• To: mathgroup at smc.vnet.net
• Subject: [mg35145] Re: [mg35137] ConstrainedMin with negative variables
• From: Rob Pratt <rpratt at email.unc.edu>
• Date: Wed, 26 Jun 2002 01:09:15 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```On Tue, 25 Jun 2002, Markus KolXchter wrote:

> Hello ng,
>
> I'm trying to implement the method of Zoutendijk, which is to solve a
> nonlinear programming problem.
> Therefor I have to solve linear subproblems with the simplex method.
> But the Mathematica function "ConstrainedMin" assumes that all variables are
> non-negative.
>
> For example, I have the following input:
>
>     ConstrainedMin[-7/3 x1 - 13/3 x2, {x1 + 5 x2 <= 0, -1 <= x1 <= 1, -1 <=
> x2 <= 1}, {x1, x2}]
>
> The Mathematica output is:
>
>     {0, {x1 -> 0, x2 -> 0}}
>
> I think the proper result should be {-22/15, {x1 -> 1, x2 -> -1/5}}.
>
> If anyone has an idea, please let me know!
>
> Regards,
>
> Markus Kolöchter

Perform a change of variables, replacing x1 with y1 - 1 and x2 with
y2 - 1.  Then the new objective function is still linear, and the new
variables are nonnegative.

Rob Pratt
Department of Operations Research
The University of North Carolina at Chapel Hill

rpratt at email.unc.edu

http://www.unc.edu/~rpratt/

```

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