Function of loss in R

Question

I have function of loss given for a k-elements vector by the following formula:

Where p is a positive parameter. I have to write a function in R which returns the value of u which minimizes this function. How can I do that?

Answer 1

first define the function you want to minimize:

my_function <- function(u) {
    ...
}

Then you can call the optim() function:

result <- optim(starting_point_for_u, my_function, ...)
# parameter value minimizing the function
result$par
# minimal value of function
result$value