Re: about ConstrainedMin

*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). Could you give me some more information or suggestions about it? 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 Subject: [mg29855] [mg29806] about ConstrainedMin > >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 > > >

**Follow-Ups**:**Re: Re: about ConstrainedMin***From:*Daniel Lichtblau <danl@wolfram.com>