[Numpy-discussion] hairy optimization problem

Mathew Yeates myeates@jpl.nasa....
Thu May 7 08:57:00 CDT 2009

David Huard wrote:
> Hi Mathew,
> You could use Newton's method to optimize for each vi sequentially. If 
> you have an expression for the jacobian, it's even better.
Here's the problem. Every time f  is evaluated, it returns a set of 
values. (a row in the matrix) But if we are trying to find the minimum 
of the first column, we only care about the first value in the set. This 
is really N optimization. problems I want to perform simultaneously.

Find N (x,y) values where x1,y1 minimizes f in the first column, x2,y2 
minimizes f in the second column, etc.
And ... doing this a column at a time is too slow (I just did a quick 
calculation and my brute force method is going to take 30 days!)

> What I'd do is write a class with a method f(self, x, y) that records 
> the result of f(x,y) each time it is called. I would  then sample very 
> coarsely the x,y space where I guess my solutions are. You can then 
> select the x,y where v1 is maximum as your initial point for Newton's 
> method and iterate until you converge to the solution for v1. Since 
> during the search for the optimum your class stores the computed 
> points, your initial guess for v2 should be a bit better than it was 
> for v1, which should speed up the convergence to the solution for v2, 
> etc.
> If you have multiple processors available, you can scatter function 
> evaluation among them using ipython. It's easier than it looks.
> Hope someone comes up with a nicer solution,
> David
> On Wed, May 6, 2009 at 3:16 PM, Mathew Yeates <myeates@jpl.nasa.gov 
> <mailto:myeates@jpl.nasa.gov>> wrote:
>     I have a function f(x,y) which produces N values [v1,v2,v3 .... vN]
>     where some of the values are None (only found after evaluation)
>     each evaluation of "f" is expensive and N is large.
>     I want N x,y pairs which produce the optimal value in each column.
>     A brute force approach would be to generate
>     [v11,v12,v13,v14 ....]
>     [v21,v22,v23 .......    ]
>     etc
>     then locate the maximum of each column.
>     This is far too slow ......Any other ideas?
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