R Optimx error : Cannot evaluate function at initial parameters

[Cassiopeia1]

Hey!

I have a project that involves estimating parameters for a Lee_Carter model (mx = exp(ax + bx *kt)). The aim is to predict future values of Life expectancy at birth (e0) without having the Kt parameter, my instructor told me I could use the optimx package to minimize e0_estimated - e0_expert (that I have values for), I first started to look for an equation for e0_estmated starting from the generic Lee_Carter Model which is why I've computed various conversions.

Whenever I run the optimization process using optimx, I keep getting an error message that says:

"Error in optimx.check(par, optcfg$ufn, optcfg$ugr, optcfg$uhess, lower, : Cannot evaluate function at initial parameters."

here's a shortened version of the code I'm working with

# Shortened matrices ax et bx
ax <- c(-4.3198094, -5.8995814, -6.1240039, -7.0870399, -7.0525417)
bx <- c(0.04522097, 0.02488256, 0.02452534, -3.2110186, -3.0955417)

data <- data.frame(
  DATE = as.Date(c("2019-01-01", "2020-01-01", "2021-01-01", "2022-01-01", "2023-01-01")),
  LE = matrix(c(77.76000, 77.05507, 76.34821, 75.64329, 74.93836), ncol = 1)
)
e0_expert <- data$LE

# Convert mx to qx
convert1 <- function(mx, qx, ax, bx, kt) {
  mx <- exp(ax + kt * bx)
  qx <- (2 * mx) / (2 + mx)
  return(qx)
}

# Calculate lx using qx
calculate_lx <- function(qx, l0 = 10000) {
  n <- length(qx)
  lx <- numeric(n) 
  lx[1] <- l0
  lx[2] <- l0 * (1 - qx[1])
  for (i in 2:n) {
    lx[i] <- lx[i - 1] * (1 - qx[i - 1])
  }
  return(lx)
}

# Convert lx to dx
calculate_dx <- function(dx, lx) {
  d0 <- l0 - lx[2]
  n <- length(lx)
  dx <- numeric(n)
  dx[1] <- d0
  for (i in 2:(n-1)) {
    dx[i] <- lx[i] - lx[i+1]
  }
  return(dx)
}

# Convert dx to Lx
calculate_Lx <- function(Lx, dx) {
  L0 <- d0 * lx[2] + 0.5
  n <- length(dx)
  Lx <- numeric(n)
  Lx[1] <- L0
  for (i in 2:n-1){
    Lx[i] <- dx[i] * lx[i+1] + 0.5
  }
  return(Lx)
}

# Convert qx to ex
convert2 <- function(Lx, lx, ex) {
  n <- length(Lx)
  ex <- numeric(n)
  ex <- sum(Lx) / lx
  e0_estime <- ex[1]
  return(e0_estime)
}

# Function to calculate the difference between the estimation and the projection
calculate_error <- function(kt, e0_expert, ax, bx) {
  e0_estime <- convert2(Lx, lx, e0_estime)
  error <- e0_estime - e0_expert
  error_value <- sum(error^2)
  cat("Error:", error_value, "\n")
  if (error_value < 50) { 
    cat("Converged to a solution: kt =", kt, "Error =", error_value, "\n")
  }
  return(error_value)
}

# Perform optimization using the defined function and parameters
result <- optimx(
  par = c(72.047557, 70.373062, 66.536728, 63.807676,   58.721023),
  fn = calculate_error, 
  e0_expert = e0_expert, 
  ax = ax, 
  bx = bx, 
  method = "Nelder-Mead",
  control = list(trace = 2, maxit = 1000, abstol = 1e-100, minimize = TRUE)
)

# kt optimal
optimal_kt <- result$par

cat("Optimal_kt:", optimal_kt, "\n")

I've tried various approaches to troubleshoot this error, but it's been persisting, impeding my progress, and I have no idea where the problem may lie (i'm quite new to R, might explain why)