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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, 20 Jun 94 13:45:42 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).

>or has anyone
>written a package that will solve this problem (linear constraints and
>nonlinear functions)
>

There doesn't seem to be anything on MathSource.

>He tried the nonlinear solver in Excel, but it doesn't return the
>optimium.... so he's looking for other ideas.

Not a good sign.  Excel uses the GRGII algorithm, which is pretty highly
regarded as a general solver (can't speak to the specific implementation in
Excel, though).  Is the objective smooth and convex (minimizing) or concave
(maximizing)?  If not, he's got problems.

> RSVP to this email address
>and I'll forward the responses to him.
>

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* 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    *
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Mathematicians are like Frenchmen:  whenever you say something to them,
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entirely different.                                    J. W. v. GOETHE