• To: mathgroup at smc.vnet.net
• Subject: [mg29855] Re: [mg29806] about ConstrainedMin
• From: qing.cheng at icos.be
• Date: Sat, 14 Jul 2001 01:36:45 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```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

cc:

Subject: [mg29855]  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

>
>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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