[SciPy-user] optimization advice needed

Neal Becker ndbecker2@gmail....
Sun Jan 27 07:06:53 CST 2008

Let me try to address the questions (to the extent that I know the answers):
I believe f(a,b) is convex.
Why not just iteratively solve for each observation?  2 reasons.  First,
because it is too computationally expensive in this application.  Second,
because each observation is noisy, so you don't want to adapt the model to
optimize just one observation.
I think Gaussian noise is a good model here.

For the first question.  The values of the parameters, which I called (a,b),
but in general we might need more variables, are more-or-less constant over
time, but change very slowly with respect to the observations.  I guess
you're asking if there is a model for how they change over time?  No, only
that they change very slowly.

dmitrey wrote:

> I guess you should specify your problem more exactly in mathematical
> terms. Does it belong to ordinary LSP, or maybe it's better to consider as
> AR, ARX, ARMA, ARMAX? Does previous a, b values affect next?
> Why couldn't you just solve the problem for each new vector of
> observations? Does the number of observations sufficiently more than
> number of vars (= num(a,b)=2)?
> Is f(a,b) convex?
> Does the noise really has Gaussian distribution? If no, least squares
> can be not a best decision.
> Would you answer the questions, it will be easier for others to give
> advices.
> As for me, I'm not skilled enough in optimal control problems to comment
> this.
> Regards, D.
> Neal Becker wrote:
>> I have an optimization problem that doesn't quite fit in the usual
>> framework.
>> The problem is to minimize the mean-square-error between a sequence of
>> noisy observations and a model.
>> Let's suppose there are 2 parameters in the model: (a,b)
>> So we observe g = f(a,b) + n.
>> Assume all I know about the problem is it is probably convex.
>> Now a couple of things are unusual:
>> 1) The problem is not to optimize the estimates (a',b') one time - it is
>> more of an optimal control problem.  (a,b) are slowly varying, and we
>> want to continuously refine the estimates.
>> 2) We want an inversion of the usual control.  Rather than having the
>> optimization algorithm call my function, I need my function to call the
>> optimization.  Specifically I will generate one _new_ random vector of
>> observations.  Then I want to perform one iteration of the optimization
>> on
>> this observation.  (In the past, I have adapted the simplex algorithm to
>> work this way).
>> So, any advice on how to proceed?
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