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Re: ConstrainedMin with negative variables

• To: mathgroup at smc.vnet.net
• Subject: [mg35164] Re: [mg35137] ConstrainedMin with negative variables
• From: Brett Champion <brettc at wolfram.com>
• Date: Thu, 27 Jun 2002 00:23:36 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

On Tuesday, June 25, 2002, at 06:55  PM, Markus Kolöchter 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!

Using the just released Mathematica 4.2:

	In[1]:= Experimental`Minimize[{-7/3 x1 - 13/3 x2, {x1 + 5 x2 <= 0, 
-1 <= x1 <= 1,
			-1 <= x2 <= 1}}, {x1, x2}]//InputForm

	Out[1]//InputForm= {-22/15, {x1 -> 1, x2 -> -1/5}}

and

	In[2]:= <<NumericalMath`NMinimize`

	In[3]:= NMinimize[{-7/3 x1 - 13/3 x2, {x1 + 5 x2 <= 0, -1 <= x1 <= 1,
			-1 <= x2 <= 1}}, {x1,x2}]

	Out[3]= {-1.46667, {x1 -> 1., x2 -> -0.2}}


Note that Minimize and NMinimize have arguments that are slightly 
different from ConstrainedMin.
Both Minimize and NMinimize use the improved LinearProgramming command 
for linear problems.

Hope this helps.

Brett Champion