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MathGroup Archive 1994

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Re: nonlinear optimization routines?

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Re: nonlinear optimization routines?
  • From: rubin at msu.edu (Paul A. Rubin)
  • Date: Mon, 27 Jun 94 10:45:21 EDT

>>>I have an office mate who is searching for a Mma package which will solve
>>>optimization problem with linear constraints and a nonlinear objective
>>>functions (i.e. the solution space is convex). There are only 10 decision
>>>variables but he needs solve the problem for lots of cases (so it would be
>>>helpful if he could execute the package from within a loop).
>>>
>>>Does anyone know if the standard packages will do this
>
>>The built-in FindMinimum routine is for unconstrained problems of a single
>>variable, while LinearProgramming and ConstrainedMax/ConstrainedMin are for
>>linear programs (so they cannot handle nonlinear objectives).
>
>
>Not the last time I checked:
>
>In[1]:= FindMinimum[(x-1)^2 + 100 (y - x^2)^2, {x, -1}, {y, 1}]
>
>		   -11
>Out[1]= {2.74586 10   , {x -> 0.999997, y -> 0.999993}}
>
>
>Jerry B. Keiper
>keiper at wri.com
>
Oops.  I should not have said that FindMinimum takes a single variable.  In
fact, you technically can use it for the constrained problem, using either
penalty or barrier methods.  You won't get exactly the optimum, but in
theory you will get close.  If memory serves, "active set" methods (which
deal with the constraints directly) are generally preferred to penalty or
barrier methods for performance.  Then again, if you're restricted to Mma
and there is (apparently) no nonlinear programming package, a bird in the
hand may be better than two in the bushes.

Paul

**************************************************************************
* Paul A. Rubin                                  Phone: (517) 336-3509   *
* Department of Management                       Fax:   (517) 336-1111   *
* Eli Broad Graduate School of Management        Net:   RUBIN at MSU.EDU    *
* Michigan State University                                              *
* East Lansing, MI  48824-1122  (USA)                                    *
**************************************************************************
Mathematicians are like Frenchmen:  whenever you say something to them,
they translate it into their own language, and at once it is something
entirely different.                                    J. W. v. GOETHE






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