• To: mathgroup at smc.vnet.net
• Subject: [mg29869] Re: [mg29806] about ConstrainedMin
• From: "Mark Harder" <harderm at ucs.orst.edu>
• Date: Sat, 14 Jul 2001 01:37:01 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Qing,
I'm afraid I don't know how the Simplex  algorithm has been "enhanced" .
This is a question that someone @ Wolfram should answer.
-mark harder

-----Original Message-----
From: qing.cheng at icos.be <qing.cheng at icos.be>
To: mathgroup at smc.vnet.net
Subject: [mg29869] Re: [mg29806] about ConstrainedMin

>
>
>Thank you, Mark.
>
>But I would like to know what ConstrainedMin inside does, not only the
>usage.
>The problem was rised from one of our applications. There we need to
>measure the position of each pins in a leads component(electronic chip).
>Based on these individual points, we need to calculate a plane, which
>should reflect a physical plane where the component can 'sit' stably, so
>call it seating plane. One way we try to  achieve this is to convert this
>problem to a LP problem. The objective function is to Minimize the Sum
>distance between the measurement points and the plane.
>We have implemented a Simplex method besed on the algorithm in Numerical
>Recipes to solve this linear problem, and found it worked not very well for
>">=" type constraints. I also brought the same problem to Mathematica, and
>found the situation that BasicSimplex failed as same as our C
>implementation, while ConstrainedMin found good solution. Now, we have done
>a data transformation before pass them to Simplex algorithm to ensure that
>all the constraints are "<=". It works in that way. But still I would like
>to know how ConstrainedMin improved BasicSimplex. (In Mathematica hand book
>from Stephen Wolfram, page 1061 says that ConstrainedMax and related
>function use an enhanced version of the simplex algorithm).
>
>
>
>Best Regards.
>
>
>/Qing
>
>
>
>
>
>
>
>
>
>"Mark Harder" <harderm at ucs.orst.edu> on 07/12/2001 10:34:41 PM
>
>To:   <qing.cheng at icos.be>, <mathgroup at smc.vnet.net>
>cc:
>
>Subject: [mg29869]  Re: [mg29806] about ConstrainedMin
>
>
>Qing,
>    For minimization of linear functions with linear constraints, see the
>function ConstrainedMin:
>
>In[413]:=
>ConstrainedMin[2 x - 3 y, {x + y < 10, x - y > 2, x > 1}, {x, y}]
>
>Out[413]=
>{0, {x -> 6, y -> 4}}
>
>In[416]:=
>ConstrainedMin[2 x - 3 y, {x + y == 12, x - y > 2, x > 1}, {x, y}]
>
>Out[416]=
>{-1, {x -> 7, y -> 5}}
>
>-mark harder
>
>
>-----Original Message-----
>From: qing.cheng at icos.be <qing.cheng at icos.be>
To: mathgroup at smc.vnet.net
>To: mathgroup at smc.vnet.net <mathgroup at smc.vnet.net>
>Date: Tuesday, July 10, 2001 10:44 PM
>
>
>>
>>Dear Mathgroup,
>>
>>Is there possibilities that I can have the implementation of
>ConstrainedMin
>>or the description of the algorithm. I find it's much more efficient than
>>classical simplex method and would like to use it in our application.
>>
>>Many thanks.
>>
>>
>>QingCheng.
>>
>>
>>My e-mail address is qing.cheng at icos.be
>>
>>
>>
>
>
>
>
>

```

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