R. Add conditions within optimization function - r

Question

I have the following optimization function, similar as this one:
R. Run optimization function in data frame:
main <- function(p1, p2, n1, n2, pE) {
# FIND MINIMUM a
func <- function(a) {
Mopt <- (p1-a*pE)/(1-a)
f_n <- (Mopt-p2)^2-Mopt*(1-Mopt)/(n1-1) - p2*(1-p2)/(n2-1)
f_d <- Mopt*(1-p2)+p2*(1-Mopt)
f_v <- f_n/f_d
}
opt <- optimize(func, seq(0, 1,by=0.01), maximum=FALSE)$minimum
}
Here, the arguments of "main" are columns from a data frame. The function returns the minimum value of "a" required to get the minimum f_v value. I would like to add some conditions to the function, or in other words, to force a certain objects to acquire values within a certain range, in order to get the minimum f_v. For instance, Mopt must follow:
0 < Mopt < 1
and (1 - a) must follow:
(1 - a) > 0.
I am not sure how to do this in the context of an optimization.

Answer 1

I think simply add the condition would work. Code might be like this.
func <- function(a) {
a = min(a, 1-1e-7);
Mopt <- max(min((p1-a*pE)/(1-a), 1-1e-7), 1e-7);
#here means a<1 and 0<Mopt<1. 1e-7 ensures the inequality. It can be 1e-6 or 1e-8 depends on the precision you need
f_n <- (Mopt-p2)^2-Mopt*(1-Mopt)/(n1-1) - p2*(1-p2)/(n2-1)
f_d <- Mopt*(1-p2)+p2*(1-Mopt)
f_v <- f_n/f_d
}
opt <- seq(0, 1, 1e-7)[which.min(sapply(seq(0, 1, 1e-7), func))]
Addition:
Code above would return the right $objective but may fail in searching minimum. To search minimum, the function should be.
func <- function(a) {
if ((1-a)<1e-7) return(Inf);
#Ensure the optimization is reached in the range of condition
Mopt <-(p1-a*pE)/(1-a);
if (Mopt<1e-7 || Mopt>(1-1e-7)) return(Inf);
#Ensure the optimization is reached in the range of condition
f_n <- (Mopt-p2)^2-Mopt*(1-Mopt)/(n1-1) - p2*(1-p2)/(n2-1)
f_d <- Mopt*(1-p2)+p2*(1-Mopt)
f_v <- f_n/f_d
}
opt <- seq(0, 1, 1e-7)[which.min(sapply(seq(0, 1, 1e-7), func))]
It is very time consuming but available when you do not need to repeat the computation for many times.