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Re: Optimizing unknown function with incomplete set of variables.

From: Olaf Till
Subject: Re: Optimizing unknown function with incomplete set of variables.
Date: Thu, 22 Dec 2016 10:11:37 +0100
User-agent: Mutt/1.5.23 (2014-03-12)

On Thu, Dec 22, 2016 at 10:05:13AM +0100, Olaf Till wrote:
> On Wed, Dec 21, 2016 at 09:00:31PM -0800, hale812 wrote:
> > I am building a set of filters combined in a circuit with no explicit
> > relation for cut-off frequencies.
> > 
> > Instead, I am building a cost function F with a set of parameters F(var1,
> > var2, freq1, freq2,....)
> > Basically, the cost F is a sum of all partial costs univariate of partial
> > filters by the *absolute* value. F=∑(|Fi|). So I expect the problem converge
> > with F=0|Fi=0.
> > 
> > freq1, freq2 and everything coming after them are CONSTANTS passed by a
> > problem generator.
> > 
> > var1, var1 are to be found.
> > It is possible to guess initial values of var1 and var2 basing on partial
> > analysis of F components.
> > 
> > I am stuck with Octave standard tool set. Seems like most tools treat
> > strictly canonical polynomial problems, simple first-order sum of scalars.
> > There is minimization tool that treat F(x) with x as all-variables vector.
> > 
> > And I did not find a way to optimize/minimize/ my problem with both
> > variables and constants passed to F.
> > 
> > Can you please help me with a way to solve this?
> For an example for passing constants to F, see section 11.11.2 of
> Octave documentation, e.g by typing 'doc ("Anonymous Functions")' from
> the Octave prompt and navigating to "Anonymous Functions".
> If all Fi can assume the value of zero, you could replace F with a
> function which returns a vector of all Fi (not their absolute value)
> and use the zero finder 'fsolve'.
> For the case a zero finder is not applicable:
> It is often problematic to optimize absolute values, because of the
> discontinuities they introduce. Consider taking the square
> instead. Then you can use 'sqp' in core Octave or 'nonlin_min' in
> optim, but it is probably better to let F return a vector of the
> squares and use 'nonlin_residmin' in optim.

Sorry, what a nonsense of me: not a vector of squares, but a vector of
the original Fi (not their absolute value and not their squares).


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