Object missing when using optim function

Question

This is my first time using the optim function in R, and I am having some trouble figuring out what I am doing wrong.

I want to find the maximum for the phi function. I am optimizing over the vector C.

Phi <- function(C, mu, sigma, xbar, P, alpha){
  X <- xbar+ P%*%C
  return(mu %*% X - alpha * t(X) %*% sigma %*% X)
}

mu, sigma, xbar, P, and alpha are predefined scalars, vectors, and matrices.

The gradient for the phi function is:

Gradient <- function(C, mu, sigma, xbar, P, alpha){
  X <- xbar+P%*%C
  n <- length(C)
  grad <- rep(0,n)
  for(j in 1:n){
    grad[j] <- mu - 2*alpha*t(X) %*% sigma
  }
  return(grad)
}

I tried using the optim function as below:

results <- optim(par = start, fn = Phi, gr = Gradient, method = "CG")

"start" is a predefined vector with the same dimensions for C.

However, when I try running the optim function, I get the following error:

> results <- optim(par = start, fn = Phi, gr = Gradient, method = "CG")
Error in xbar + P %*% C : 'xbar' is missing

What am I doing wrong? I would appreciate any guidance! Thanks in advance.

Edit: I defined my start vector as such-

Start <- function(n){
  vector <- rep(1/n, n)
  return(vector)
}

start <- Start(length(mu)-1)

Answer 1

As correctly stated by @Maciej, you have additional parameters mu, sigma, xbar, P, alpha, which are declared, but not supplied to an optim() call.

To supply these parameters, an ellipsis ... can be used, where you specify them in a form name=value.

Here's a small example of how a function with parameters can be optimized:

f <- function(x, param) sum((x-param)^2)
optim(par=c(0,0,0), fn=f, param=1:3)
$par
[1] 1.000538 1.999985 2.999919

$value
[1] 2.966097e-07

$counts
function gradient 
     112       NA 

$convergence
[1] 0

$message
NULL