Setting up non-linear optimization in R

Question

I have a function that calculates the 'value' of a model based on the inputs.

ModelValue <- function(x, y, z) { #long, most likely non-linear stuff return(Value)}

x takes is a number between 0-1, and is fixed based on the model I'm testing. Ie, x will just happen to be 0.56.

y and z are groups of 4 thresholds that I want to optimize to maximize Value.

y=c(pa, pb, pc, pd) and z=c(ta, tb, tc, td), subject to: all are => 0.001, all are =<0.997, pa + pb + pc + pd == 1; and ta + tb + tc + td == 1

I've tried looking at optimx and spg; (this is as far as I could get) but no matter what I do, I can't seem to create an optimization function that doesn't freak out as soon as I try and mention pa, pb, pc etc. I don't understand how to tell the model what variables its meant to be optimizing...

OptimizeModel <- function(x) { p0=1 #initial guess fn = ModelValue(x, y, z) lo <- c(0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001) # lower limits for parameters hi <- c(0.997, 0.997, 0.997, 0.997, 0.997, 0.997, 0.997, 0.997) # upper limits for parameters y<- c(pa, pb, pc, pd) z<- c(ta, tb, tc, td) pa + pb + pc + pd = 1 ta + tb + tc + td = 1 # pa > 0.001 # pb > 0.001 # pc > 0.001 # pd > 0.001 # ta > 0.001 # tb > 0.001 # tc > 0.001 # td > 0.001 ans1 <- spg(par=p0, fn=fn, lower=lo, upper=hi, control=list(maximize=TRUE, trace=FALSE)) return (ans1) }

When I try it:

OptimizeModel(0.56) #Error in OptimizeModel(0.56) : object 'pa' not found

Erwin Kalvelagen · Accepted Answer · 2020-06-14 09:27:35Z

Just pass on pa,pb,pc to spg and use them in the function evaluation. The documentation of spg is showing an example where this is done:

valley.f <- function(x, cons) { ...}

Here x are the decision variables and cons is extra data (constants).

The call to spg looks like:

ans.spg2 <- spg(par=p0, fn=valley.f, cons=k, method=2)

You see cons=k is specified. This argument is not for spg itself but is passed on to the function evaluation (and gradient evaluation) functions. You need to do the same for pa,pb,pc.

See: https://www.rdocumentation.org/packages/BB/versions/2019.10-1/topics/spg

Unfortunately, I spent several hours trying to follow the example and still don't understand how to apply it to my situation.
That is sad. This is not complicated, and the examples are quite good.

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