Errror: $ not suitable to atomic vectors

Question

I need to write a computer program which would look for whether two functions have the same minima points for given parameters, so I wanted to write program which would look for this on some example functions, which minima I know. So I wrote a program, but I get an error 'result$hessian':$ operator is invalid for atomic vectors all the time. But for these given examples, the hessian should be positive, defined, and definitelly non atomic. I don't know whether algorithm get stuck at local minimum or something. Here is the code:

find_min <- function(f) {

  n_starts <- 10
  
  min_points <- rep(NA, n_starts)
  
 
  success <- FALSE
  
  
  for (i in 1:n_starts) {
    
    result <- tryCatch(optim(par = runif(3, min = -100, max = 100), function(x) -f(x), method = "L-BFGS-B", lower = -100, upper = 100, hessian = TRUE),
                       error = function(e) {
                         
                         success <- FALSE
                       })
    if (!is.null(result$hessian) && is.matrix(result$hessian) && any(eigen(result$hessian)$values <= 0)) {
      min_points[i] <- NA
      success <- FALSE
    }
   
    if (is.null(result$hessian)) {
      min_points[i] <- NA
      success <- FALSE
    }
   
    if (is.na(result$par) || !is.numeric(result$par)) {
      min_points[i] <- NA
      success <- FALSE
    }
    
    min_points[i] <- result$par
    success <- TRUE
  }
  
 
  if (any(!is.na(min_points))) {
    return(min_points[which.min(sapply(min_points, f))])
  } else {
    return(NA)
  }
}


# example functions
f1 <- function(x) {
  x[1]^2 + x[2]^2 + x[3]^2
}

f2 <- function(x) {
  x[1]^4 + x[2]^4 + x[3]^4
}

min1 <- find_min(f1)
min2 <- find_min(f2)

if (is.na(min1[2]) || is.na(min2[2])) {
  print(min1[1])
  print(min2[1])
} else if (all(min1[2] == min2[2])) {
  print("The minimum points are the same.")
} else if (!all(min1[2] == min2[2])) {
  print("The minimum points are different.")

I tried to make sure that hessian is not an atomic vector by trying to catch some errors. I tried to use different starting points in order to get function unstuck if it is stuck at local minima. I tried giving it different example equations. I tried checking the order of if's in hessian checking. Tried to check if is.atomic throws out something but it doesn't even want to compile that. Please help because nothing worked...

Answer 1

result$par are the 3 parameters that optim was initialised with each time; yet you were attempting to place those at a single location of numeric vector (min_points); this is invalid. but it seems to be not what you say what you wish to do any way. you are not seeking the min_points you are surely seeking the min_values (reached by whatever points)

i.e. min_points[i] <- result$value

you can then end the function by returning the minimum of min_points directly.

... 
    min_points[i] <- result$value
    success <- TRUE
  }
 
  min(min_points)
}

of course you would probably want to go back and rename min_points to min_vals or whatever you think is descriptive. making these recommended changes and given your examples results in the following

> min1
[1] -30000
> min2
[1] -3e+08