# [Numpy-discussion] N dimensional dichotomy optimization

Charles R Harris charlesr.harris@gmail....
Wed Nov 24 11:18:58 CST 2010

```On Tue, Nov 23, 2010 at 3:37 AM, Sebastian Walter <
sebastian.walter@gmail.com> wrote:

> On Tue, Nov 23, 2010 at 11:17 AM, Gael Varoquaux
> <gael.varoquaux@normalesup.org> wrote:
> > On Tue, Nov 23, 2010 at 11:13:23AM +0100, Sebastian Walter wrote:
> >> I'm not familiar with dichotomy optimization.
> >> Several techniques have been proposed to solve the problem: genetic
> >> algorithms, simulated annealing, Nelder-Mead and Powell.
> >> To be honest, I find it quite confusing that these algorithms are
> >> named in the same breath.
> >
> > I am confused too. But that stems from my lack of knowledge in
> > optimization.
> >
> >> Do you have a continuous or a discrete problem?
> >
> > Both.
> >
> >> Is your problem of the following form?
> >
> >> min_x f(x)
> >> s.t.   lo <= Ax + b <= up
> >>            0 = g(x)
> >>            0 <= h(x)
> >
> > No constraints.
>
> didn't you say that you operate only in some convex hull?
>
> >
> >> An if yes, in which space does x live?
> >
> > Either in R^n, in the set of integers (unidimensional), or in the set of
> > positive integers.
> According to  http://openopt.org/Problems
> this is a mixed integer nonlinear program http://openopt.org/MINLP . I
> don't have experience with the solver though,
> but it may take a long time to run it since it uses branch-and-bound.
> In my field of work we typically relax the integers to real numbers,
> perform the optimization and then round to the next integer.
> This is often sufficiently close a good solution.
>
>
I've sometimes applied a genetic algorithm to the rounding, which can
improve things a bit if needed.

Chuck
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