Suppose I want to minimize the following function:
-(5-(x1-2)^2-2*(x2-1)^2)
s.a. x1+4*x2 < 3
For unrestricted optimization problems I can use the following code.
fr <- function(x){
x1 <- x[1]
x2 <- x[2]
-(5-(x1-2)^2-2*(x2-1)^2)
}
optim(c(1,1),fr)
How to optimize with the constraint?
I'm learning Portuguese, but this is a solution without inf explicit.
ui = c(-1, -4)
ci = c(-3)
fr <- function(x) {
x1 = x[1]
x2 = x[2]
-(5-(x1-2)^2-2*(x2-1)^2)
}
constrOptim(c(1.6,.2), fr, ui=ui, ci=ci, method='Nelder-Mead')
$par
[1] 1.6668 0.3333
$value
[1] -4
$counts
function gradient
192 NA
$convergence
[1] 0
$message
NULL
$outer.iterations
[1] 3
$barrier.value
[1] -0.000
In this example, you can define in the function that, if the values exceed the constraint, it gets infinite value:
fr <- function(x){
if(x[1]+4*x[2] > 3 ){value<-Inf}
else{
x1 <- x[1]
x2 <- x[2]
-(5-(x1-2)^2-2*(x2-1)^2)
}
}
Solving:
optim(c(1,0),fr)
$par
[1] 1.6666193 0.3333452
$value
[1] -4