GRG Non-Linear Least Squares (Optimization) - r

Question

I am trying to convert an Excel spreadsheet that involves the solver function, using GRG Non-Linear to optimize 2 variables that return the lowest sum of squared errors. I have 4 known times (B) at 4 known distances(A). I need to create an optimization function to find what interaction of values for Vmax and Tau produce the lowest sum of squared errors. I have looked at the nls function and nloptr package but can't quite seem to piece them together. Current values for Vmax and Tau are what was determined via the excel solver function, just need to replicate in R. Any and all help would be greatly appreciated. Thank you.
A <- c(0,10, 20, 40)
B <- c(0,1.51, 2.51, 4.32)
Measured <- as.data.frame(cbind(A, B))
Corrected <- Measured
Corrected$B <- Corrected$B + .2
colnames(Corrected) <- c("Distance (yds)", "Time (s)")
Corrected$`X (m)` <- Corrected$`Distance (yds)`*.9144
Vmax = 10.460615006988
Tau = 1.03682513806393
Predicted_X <- c(Vmax * (Corrected$`Time (s)`[1] - Tau + Tau*exp(-Corrected$`Time (s)`[1]/Tau)),
Vmax * (Corrected$`Time (s)`[2] - Tau + Tau*exp(-Corrected$`Time (s)`[2]/Tau)),
Vmax * (Corrected$`Time (s)`[3] - Tau + Tau*exp(-Corrected$`Time (s)`[3]/Tau)),
Vmax * (Corrected$`Time (s)`[4] - Tau + Tau*exp(-Corrected$`Time (s)`[4]/Tau)))
Corrected$`Predicted X (m)` <- Predicted_X
Corrected$`Squared Error` <- (Corrected$`X (m)`-Corrected$`Predicted X (m)`)^2
#Sum_Squared_Error <- sum(Corrected$`Squared Error`)

Answer 1

is your issue still unsolved?
I'm working on a similar problem and I think I could help.
First you have to define a function that will be the sum of the errors, which has for variables Vmax and Tau.
Then you can call an optimisation algorithm that will change these variables and look for a minimum of your function. optim() might be sufficient for your application, but here is the documentation for nloptr:
https://www.rdocumentation.org/packages/nloptr/versions/1.0.4/topics/nloptr
and here is a list of optimisation packages in R:
https://cran.r-project.org/web/views/Optimization.html
Edit:
I quickly recoded the way I would do it. I'm a beginner, so it's probably not the best way but it still works.
A <- c(0,10, 20, 40)
B <- c(0,1.51, 2.51, 4.32)
Measured <- as.data.frame(cbind(A, B))
Corrected <- Measured
Corrected$B <- Corrected$B + .2
colnames(Corrected) <- c("Distance (yds)", "Time (s)")
Corrected$`X (m)` <- Corrected$`Distance (yds)`*.9144
#initialize values
Vmax0 = 15
Tau0 = 5
x0 = c(Vmax0,Tau0)
#define function to optimise: optim will minimize the output
f <- function(x) {
y=0
#variables will be optimise to find the minimum value of f
Vmax = x[1]
Tau = x[2]
Predicted_X <- Vmax * (Corrected$`Time (s)` - Tau + Tau*exp(-Corrected$`Time (s)`/Tau))
y = sum((Predicted_X - Corrected$`X (m)`)^2)
return(y)
}
#call optim: results will be available in variable Y
Y<-optim(x0,f)
If you type Y into the console, you will find that the solver finds the same values as Excel, and convergence is achieved.
In R, there is no need to define columns in data frames with brackets as you did, instead use vectors. You should probably follow a tutorial about this first.
Also it is misleading that you set inital values as values that were already the optimal ones. If you do this then optim() will not optimise further.
Here is the documentation for optim:
https://stat.ethz.ch/R-manual/R-devel/library/stats/html/optim.html
and a tutorial on how to use functions:
https://www.datacamp.com/community/tutorials/functions-in-r-a-tutorial
Cheers