ZERO

but this was very helpful

I actually have to run

well thanks for the discussion

ok

also I expect that my constraints will be highly nonlinear, which sounds like that will be a problem?

ok

ok

ok

ok

I have kind of gotten that impression given that I haven't been able to find much

ok

but am willing to if it helps makes a convergence argument

because as of now I am not really assuming anything about them

and that's why I have also been vague about what f and c are

was kind of a checklist of criteria to need to ensure teh method convereges

and so what I was hoping to get out of my posting of the question

just none that exactly fit my problem

and I have seen many papers out there on convergence proofs

yup

be it locally or globally

and so I am not too concerned about discovering the rate of convergence but just that it has convergent properties

which really means I run the code as long as I can until I run out of computational budget

and so i do this, iterating until convergence

so I am trying to pick new points, iteratively, that I think do better at minimizing f(x) while also satisfying c(x)

ok, I need more actual evaluations from the black box simulator, let's pick the next point that we think is best. And best is judged by will this value of x return a c(x) that meets the constraint and is smaller than my previous f(x)

the next thing we do is say

but so after I build my GP surrogate models

just not theoretical

and as of now I have empirical convergence

yes

yup

and they give me prediction at new x values

I build teh surrogates because they are cheaper to evaluate and work with

but in any event

Gaussian Processes (GP's) are also a special case of a radial basis function if your more familiar with that

similar

100%

so now I have an approximation for f(x) and c(x) because in the black box world the assumption is that evaluating the true f(x) and c(x) is computationally costly

I build a surrogate model for f(x) and c(x) using a Gaussian Process

from these "inputs" (x) and "outputs" (f(x),c(x))

I start with an initial set of points x and get back f(x) and c(x)

So what I do is

and so evaluating them is trivial

so I actually do know f(x) and c(x)

Well right now I am just running it on toy examples

So I can evaluate the computer simulator

That is correct

Or the idea of a black box simulator?

Are you familiar with black box optimization?

NIce!