gradient descent pour une fonction à variable multiple

Bonjour ;
J'ai implémenter l'algorithme du gradient descent sur R :

Code:

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# Having the number of iterations, step size, and start value be parameters the
# user can alter (with sane default values) I think is a better approach than
# hard coding them in the body of the function
grad<-function(iter = 30, alpha = 0.1, x_init = 1){
 
    # define the objective function f(x) = sqrt(2+x)+sqrt(1+x)+sqrt(3+x)
    objFun = function(x) return(sqrt(2+x)+sqrt(1+x)+sqrt(3+x))
 
    # define the gradient of f(x) = sqrt(2+x)+sqrt(1+x)+sqrt(3+x)
    # Note we don't split up the gradient here
    gradient <- function(x) {
        result <- 1 / (2 * sqrt(2 + x))
        result <- result + 1 / (2 * sqrt(1 + x))
        result <- result + 1 / (2 * sqrt(3 + x))
        return(result)
    }
 
    x <- x_init
 
    # create a vector to contain all xs for all steps
    x.All = numeric(iter)
 
    # gradient descent method to find the minimum
    for(i in seq_len(iter)){
        # Guard against NaNs
        tmp <- x - alpha * gradient(x)
        if ( !is.nan(suppressWarnings(objFun(tmp))) ) {
            x <- tmp
        }
        x.All[i] = x
        print(x)
    }
 
    # print result and plot all xs for every iteration
    print(paste("The minimum of f(x) is ", objFun(x), " at position x = ", x, sep = ""))
    plot(x.All, type = "l")  
 
}

Je veux faire la meme chose pour une fonction à plusieurs variables , J'ai essayé mais ça ne marche pas :

Code:

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grad<-function(iter = 30, alpha = 0.1){
 
  # define the objective function f(x) 
  objFun = function (x,y) return((x^2+y-11)^2+(x+y^2-7)^2)
 
  # define the gradient of f(x) 
  # Note we don't split up the gradient here
  gradient <- function(x , y) {
 
    result <- c(4*x*(x^2+y-11)+2*(x+y^2-7),2*(x^2 + y - 11 )+4*y*(x+y^2-7))
 
    return(result)
  }
 
 
  result <- c(5,5)
 
  # create a vector to contain all xs for all steps
  result.All = c(iter)
 
  # gradient descent method to find the minimum
  for(i in seq_len(iter)){
    # Guard against NaNs
    tmp <- result - alpha * gradient(x,y)
    if ( !is.nan(suppressWarnings(objFun(tmp))) ) {
      result <- tmp
    }
    result.All[i] = result
    print(result)
  }
 
  # print result and plot all xs for every iteration
  print(paste("The minimum of f(x) is ", objFun(x , y), " at position x = ", result, sep = ""))
  plot(result.All, type = "l")  
 
}