Solve optimisation with double integral equation in R

Question

I have an optimisation problem that has a objective function in the form of a double integral.

The objective function is:

# define objective function
  fun_obj <- function(a) pracma::integral2(function(x,y) 
    exp(-a[1]*(x - 1/2) - a[2]*(x^2 - 1/3) - a[3]*(y - 1/2) - a[4]*(y^2 - 1/3) - a[5]*(x*y - 0.76)),
    xmin = 0,xmax = 1, ymin = 0, ymax = 1)

I tried using pracma::fminsearch, that mimics the function of same name from MATLAB.

  #solve integral
  solution <- pracma::fminsearch(fun_obj, c(1,1,1,1,-1), method="Nelder-Mead", minimize = T)

The code works in MATLAB, but I intend to make it part of a package and would like to have it all in R.

In R I keep getting a error message Error in scl * fun(x, ...) : non-numeric argument to binary operator. The function fun_obj is working correctly. When I run fun_obj(c(1,1,1,1,-1)) I get no errors and the expected result (0.729).

What is this error about and how to fix it?

Answer 1

The reason you are getting the error is that pracma::intergral2 does not return a single number. It returns a named list with two components: Q and error. Your function needs to return the Q component to work properly, since fminsearch needs to act on a function that returns a numeric output, not a named list. So you need only do:

fun_obj <- function(a) pracma::integral2(function(x,y) 
  exp(-a[1]*(x - 1/2) - a[2]*(x^2 - 1/3) - a[3]*(y - 1/2) - 
       a[4]*(y^2 - 1/3) - a[5]*(x*y - 0.76)),
  xmin = 0,xmax = 1, ymin = 0, ymax = 1)$Q


solution <- pracma::fminsearch(fun_obj, c(1,1,1,1,-1), method="Nelder-Mead", minimize = T)

solution
#> $xmin
#> [1]  203.5127  191.7917  168.6375  233.9007 -931.3801
#>
#> $fmin
#> [1] 1.023348e-112
#> 
#> $count
#> [1] 5001
#> 
#> $convergence
#> [1] 0
#>
#> $info
#> $info$solver
#> [1] "Nelder-Mead"