Question on nloptr package in for optimisation

Question

I am trying to optimize an function using nloptr package in R like below

Some_Dataframe_Fixed = data.frame(x = 1:2, y = 4:5)

eval_f <- function(x) {
  Some_Arg_Fixed_Mat = as.matrix(Some_Dataframe_Fixed)
100 * (x[2] - x[1] * x[1]) ^ 2 + (1 - x[1]) ^ 2
}

In above function, I am converting an external data frame Some_Dataframe_Fixed to matrix inside the function.

I would like to know from expert here, if such implementation is efficient? Will that dataframe Some_Dataframe_Fixed be converted fresh every time nloptr call that function during optimization? Or should I always convert that data frame outside of the function since that conversion does not depend on x?

Thanks for your pointer.

Answer 1

Such an implementation is NOT efficient, since as.matrix(Some_Dataframe_Fixed) would evaluate Some_Dataframe_Fixed everytime the function eval_f is called.

How to make it more efficient?

Evaluate only once while function is defined:

Some_Dataframe_Fixed = data.frame(x = 1:2, y = 4:5)

eval_f <- function(x, some_arg_fixed_mat=as.matrix(Some_Datframe_Fixed)) {
  100 * (x[2] - x[1] * x[1]) ^ 2 + (1 - x[1]) ^ 2
}

This lets the evaluation happen only once at function definition time.

Construct a Closure to Ensure Once Only Evaluation

Another, more general way is to use a closure - and define a function which can create for every specific Some_Dataframe_Fixed a new updated eval_f function:

# `Some_Dataframe_Fixed` here as `df`
make_eval_f <- function(df) {
  mat <- as.matrix(df)  # the as.matrix(df) call as a closure
  function(x) {
    # Use `mat` inside the function
    100 * (x[2] - x[1]^2)^2 + (1 - x[1])^2
  } # this eval_f function gets returned
}

eval_f <- make_eval_f(Some_Dataframe_Fixed)

And then you can use the eval_f function like above. When Some_Dataframe_Fixed changes, you can redefine eval_f by calling make_eval_f() with the updated dataframe.