[SciPy-user] constrained optimization
Robert Kern
robert.kern@gmail....
Mon Apr 28 13:57:41 CDT 2008
On Mon, Apr 28, 2008 at 1:34 PM, John Hunter <jdh2358@gmail.com> wrote:
> I need to do a N dimensional constrained optimization over a weight w
> vector with the constraints:
>
> * w[i] >=0
>
> * w.sum() == 1.0
>
> Scanning through the scipy.optimize docs, I see a number of examples
> where parameters can be bounded by a bracketing interval, but none
> where constraints can be placed on combinations of the parameters, eg
> the sum of them. One approach I am considering is doing a bracketed
> [0,1] constrained optimization over N-1 weights (assigning the last
> weight to be 1-sum others) and modifying my cost function to punish
> the optimizer when the N-1 input weights sum to more than one.
>
> Is there a better approach?
Transform the coordinates to an unconstrained N-1-dimensional space.
One such transformation is the Aitchison (or "additive log-ratio")
transform:
y = log(x[:-1] / x[-1])
And to go back:
tmp = hstack([exp(y), 1.0])
x = tmp / tmp.sum()
Searching for "compositional data analysis" should yield similar
transformations, but this one should be sufficient for maintaining
constraints. For doing statistics, the other have better properties.
--
Robert Kern
"I have come to believe that the whole world is an enigma, a harmless
enigma that is made terrible by our own mad attempt to interpret it as
though it had an underlying truth."
-- Umberto Eco
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