Gradient Descent Method with Backtracking Function in R - r

Question

I am trying to write a function in R to implement the gradient method with backtracking for a quadratic minimization problem min{x^T*A*x: x in R5} and A being a Hilbert matrix. The output of the function should be the number of iterations and the solution to x.
Photo of the problem here
A <- hilbert.matrix(5)
dec_gradient <- function(f, g, x_0, s, alpha, beta, epsilon) {
x <- x_0
grad <- g(x)
fun_val <- f(x)
iter <- 0
while(norm(grad) > epsilon) {
iter <- iter + 1
t <- s
while (fun_val-f(x-t*grad)<alpha*t*norm(grad)^2) {
t <- beta*t
x <- x-t*grad
fun_val <- f(x)
grad <- g(x)
print('iter_number = '+ str(iter) + ' norm_grad = ' + str(norm(grad)) + ' fun_val = ' + str(fun_val))
}
return(x, fun_val)
}
}
f<- t(x)%*%A%*%x
g <- 2*A%*%x
alpha <- 0.5
beta <- 0.5
s <- 1
epsilon <- 10e-4
# define starting point
x_0 <- matrix(c(1,2,3,4,5), ncol = 1)
dec_gradient(f, g, x_0, s, alpha, beta, epsilon)
I keep getting the error
Error in g(x) : could not find function "g"

Answer 1

I was able to (with help) write the function that worked:
dec_gradient <- function(f, g, x_0, s, alpha, beta, epsilon) {
x <- x_0
grad <- g(x)
fun_val <- f(x)
iter <- 0
while(norm(grad) > epsilon) {
iter <- iter + 1
t <- s
while ((fun_val-f(x-t*grad))<alpha*t*norm(grad)^2) {
t <- beta*t
x <- x-t*grad
fun_val <- f(x)
grad <- g(x)
}
cat(paste0('iter_number = ', iter, "\n", 'norm_grad = ', norm(grad), "\n", 'fun_val = ', fun_val, "\n"))
}
print(iter)
return(list(x, fun_val)) }
f <- function(x, .A=A) t(x) %*% .A %*% x
g <- function(x, .A=A) 2* .A %*% x
alpha <- 0.5
beta <- 0.5
s <- 1
epsilon <- 10e-4
# define starting point
x_0 <- matrix(c(1,2,3,4,5), ncol = 1)
dec_gradient(f, g, x_0, s, alpha, beta, epsilon) ```