Question

Simple one here, i once knew this but it has been lost over the years.

Simple equation easy to code in R:

f(x,y) = 2x^2 + 4y^2 + 6x - 8y + 15

And i have constraints of x > 1 and y > -1.

I cant for the life of me remember how to write the constraints properly in R and the book i have is no use

Cheers for any help

Looking for the minimum and maximum

Answer 1

Define your function that takes a single vector of arguments:

myfun <- function(xy) { 
  x <- xy[1] 
  y <- xy[2] 

  2*x^2 + 4*y^2 + 6*x - 8*y + 15
}

Supply starting values to optim and specify your lower bounds for x and y:

starting_values <- c(0, 0)
optim(starting_values, myfun, lower=c(1, -1), method='L-BFGS-B')

optim output:

$par
[1] 1 1

$value
[1] 19

$counts
function gradient 
       2        2 

$convergence
[1] 0

$message
[1] "CONVERGENCE: NORM OF PROJECTED GRADIENT <= PGTOL"