is the objective function stochastic (-> use something like patternsearch) or deterministic?

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SA-W
SA-W 2023-3-3
编辑： Torsten 2023-3-4
My objective function is given by
f(x) = ||d^sim(x) - d^exp||^2
d^exp is a constant vector of measurements, to which I add random noise utilizing randn. Then I call the optimization (lsqnonlin, fmincon, whatever,...) In particular, d^exp does not depend on the parameters x.
Since I add the noise just once a priori to the optimization, my objective function is still deterministic, right?
I just wanted to double-check that because, at least I read about that, objective functions including noise are better handled by derivative-free optimizers like patternsearch.

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Torsten
Torsten 2023-3-3
编辑：Torsten 2023-3-3
Since I add the noise just once a priori to the optimization, my objective function is still deterministic, right?
Right, but why do you add noise to your measurement data ? Aren't they noisy enough already ?
I just wanted to double-check that because, at least I read about that, objective functions including noise are better handled by derivative-free optimizers like patternsearch.
Stochastic optimization (thus optimization with an objective with random outputs) isn't possible with any tool from the optimization toolbox.
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Torsten
Torsten 2023-3-3
编辑：Torsten 2023-3-4
@SA-W
I just wanted to double-check that because, at least I read about that, objective functions including noise are better handled by derivative-free optimizers like patternsearch.
Just to add to the statement above: The measurement data (d^exp) can be noisy. The main requirement for the use of conventional deterministic optimizers is that the fitting function (d^sim) is a smooth function of the fitting parameters and the independent variable.

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