[SciPy-user] nonlinear optimisation with constraints

[Sebastian Walter]

Hello Ernest,



2009/6/22 Ernest Adrogué <eadrogue at gmx.net>:
> Hi all,
>
> I am stuck in an obnoxious optimisation problem.
>
> Essentially, I want to find the local maximum of a
> multivariate nonlinear function subject to a linear
> constraint.
>
> x = (a1, a2, a2, ..., a_n, b1, b2, b3, ..., b_n)
>
> Maximise:    f(x)
> Subject to:  sum(a) - sum(b) = 0
>
> No big deal, apparently. The problem is that f(x) is defined
> only when x_n > 0 for all n, as it contains lots of
>
> log(a[i] * b[j])
>
> which are undefined when a[i] or b[j] < 0.
>
> I have tried to specify a lower bound for x, but both
> fmin_l_bfgs_b and fmin_tnc seem to evaluate the objective
> function with elements of x < 0, regardless of the bounds
> specified, making my programme to crash.
>
> fmin_cobyla seems to ignore the constraint altogether.
>
> I have run out of ideas on how to deal with this.
> Any advice?

are you sure you can't reformulate the problem?

maybe you should try an interior point method. By definition, all
iterates will be feasible.
There is a python wrapper for IPOPT out there. It's called pyipopt. It
worked reasonably well when I tried it.
OPENOPT also interfaces to IPOPT as far as I know, but I have never
used that interface.


Sebastian


>
> Thanks.
>
> Ernest
>
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