I am working on a nonlinear Least squares (NLS) problem of the following form:
where 
are the variables to be optimized and y is the data used to fit the function. 
can take values in the range 
only.Because of the structure of the problem (let's assume this doesn't accept alternative approaches), I am currently using a gridsearch method to find a "guess" of 
to use as an input in the NLS problem in order to find 
. Here, we can think of 
as some sort of "starting point", which is used to subset data (i.e. pick relevant data) through a boolean variable and then pass that subsample to the NLS problem. In matlab, I am doing something like: NLS_objfun = @(theta)(y(idx) - f(t(idx),theta))'(y(idx) - f(t(idx),theta));
Then I minimize NLS_objfun using an optimizer.
The method works and delivers the correct values of 
with low error. However, it takes a long time. Thus, I was trying to use bayesopt to tune the parameter 
and then proceed with the NLS problem (which is really fast conditional on a guess of 
). When I am trying to implement this, I do something similar to what follows: x2 = optimizevariable('x2',[0,1],'Type','real')
fun = @(theta)NLS_objfun(theta);
results = bayesopt(fun,[x2],'Verbose',0,...
'AcquisitionFunctionName','expected-improvement-plus')
I get the following error, which of course comes from the subsetting.
Operator '>' is not supported for operands of type 'optimizableVariable'.
I was reading the bayesopt documentation, but I couldn't find more details on how to overcome this structure.
Any help is much appreciated
Thanks!
