R optim: correct using for function with more than one argument

Question

I am writing a function for minimization using optim . The task is to solve some similar optimization tasks in loop.

# K and k are always the same (they are read from a file)

K <- matrix(data = c(1, 2, 1, 2, 1, 
                 2, 16, 2, 1, 2, 
                 1, 2, 8, 2, 1,
                 2, 1, 2, 16, 2,
                 1, 2, 1, 2, 32),
        nrow = 5, ncol = 5, byrow = TRUE)

k <- c(-2, 4, 12, 0, 2)

# j will be changed

minimize <- function(beta){ #function to minimize (for beta)
value <- (1/2)*(t(beta)%*%K%*%beta) - t(k)%*%beta + j*abs(sum(beta)-n_s)
return(value)
}

myfunc <- function(K, k, m) #K is matrix, k is vector
{
   j_values <- 10^seq(-5, 5, length = m)
   for (i in 1:m)
   {
     current_j_value <- j_values[i]
     #I want to set j in minimize function as current_j_value (and also my k and K from file)
     # and then minimize it
     myans <- optim(c(0, 0, 0, 0, 0), minimize) # using minimize(K, k, j) doesn't work
     print(myans$par)
   }
}

myfunc(K, k, 5)

My question is how to give arguments to my minimize function (to create it dynamically?) and then use it in optim .

Answer 1

If youw ant to include extra parameters in you minimize function you can add these in the optim call as from the documentation see ?optim the dots ( ... ) ... Further arguments to be passed to fn and gr .

So including j , k , K and n_s in minimize

minimize <- function(beta, j, k, K, n_s){ #function to minimize (for beta)
  value <- (1/2)*(t(beta)%*%K%*%beta) - t(k)%*%beta + j*abs(sum(beta)-n_s)
  return(value)
}

and then adding these to the optim call (I have set n_s = 0 ) like,

myfunc <- function(K, k, m) #K is matrix, k is vector
{
  j_values <- 10^seq(-5, 5, length = m)
  for (i in 1:m)
  {
    current_j_value <- j_values[i]
    #I want to set j in minimize function as current_j_value (and also my k and K from file)
    # and then minimize it
    myans <- optim(c(0, 0, 0, 0, 0), minimize, j = current_j_value, k = k, K = K, n_s = 0) # using minimize(K, k, j) doesn't work
    print(myans$par)
  }
}

Running this then,

> myfunc(K, k, 5)
[1] -6.7956860  0.7999990  1.9999999  0.5333326  0.1290324
[1] -6.7911329  0.7996483  2.0000002  0.5329818  0.1290322
[1] -5.3512894  0.6889257  1.9999436  0.4222287  0.1290095
[1] -2.80295781  0.61426579  1.95348934  0.24715200 -0.01194974
[1] -1.2999142  0.4313710  1.3088572 -0.5764644  0.1361504

All the code together

# K and k are always the same (they are read from a file)

K <- matrix(data = c(1, 2, 1, 2, 1, 
                     2, 16, 2, 1, 2, 
                     1, 2, 8, 2, 1,
                     2, 1, 2, 16, 2,
                     1, 2, 1, 2, 32),
            nrow = 5, ncol = 5, byrow = TRUE)

k <- c(-2, 4, 12, 0, 2)

# j will be changed

minimize <- function(beta, j, k, K, n_s){ #function to minimize (for beta)
  value <- (1/2)*(t(beta)%*%K%*%beta) - t(k)%*%beta + j*abs(sum(beta)-n_s)
  return(value)
}

myfunc <- function(K, k, m) #K is matrix, k is vector
{
  j_values <- 10^seq(-5, 5, length = m)
  for (i in 1:m)
  {
    current_j_value <- j_values[i]
    #I want to set j in minimize function as current_j_value (and also my k and K from file)
    # and then minimize it
    myans <- optim(c(0, 0, 0, 0, 0), minimize, j = current_j_value, k = k, K = K, n_s = 0) # using minimize(K, k, j) doesn't work
    print(myans$par)
  }
}

myfunc(K, k, 5)