On Tue, Jan 29, 2008 at 08:23:36AM -0700, Robert Dodier wrote:
> On 1/29/08, Alexandre Campos <alexandre at emc.ufsc.br> wrote:
>
> > exists in maxima something to optimize a function (non-linear)
> > constrained to some equations and/or inequations ?
>
> There is augmented_lagrangian_method which can solve problems with
> equality constraints on a nonlinear objective function.
> For inequality constraints, there isn't anything in Maxima to directly
> solve such problems. Maybe you can try to rephrase the problem
> as an unconstrained problem, e.g. a constraint x > 0 could be
> translated into an unconstrained variable y = log(x). I don't know
> if that is possible in general.
>
> Or maybe the objective function is close enough to linear so you
> could apply the simplex method, which Maxima has.
>
> augmented_lagrangian_method is not the strongest method for
> problems with equality constraints. I think there are some web
> sites which describe various methods.
I find the Nocedal-Wright book (2006 is the latest edition) a great
reference for nonlinear problems. Judd, Kenneth L: Numerical methods
in economics gives a good overview in the relevant chapter.
Sometimes solving the first order conditions as a nonlinear system of
equations works for small (2-5 unknowns) systems.
Maybe if the OP posted the problem, it would be easier to help.
Nonlinear optimization problems with constraints are very tricky in
general. There exist methods for certain cases, eg convexity of the
objective function.
HTH,
Tamas