What is optimx in R

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The optimx() is a general-purpose optimization function in R that can call several other R tools for optimization, such as optim, spg, ucminf, nlm, and nlminb. It also tries to unify the calling sequence to allow several tools to use the same front end.

To install optimx, you can use the install.packages function in R with the ‘optimx’ package as an argument.

install.packages('optimx')

To load the package before using it, you can use the library() function.

library(optimx)

Example

library(optimx)

fun <- function(x) {
  x1 <- x[1]
  x2 <- x[2]
  
  return((x1 - 2)^2 + (x2 + 3)^2)
}

# Set the optimization parameters
start_vals <- c(0, 0)
method <- "Nelder-Mead"

# Run the optimization
result <- optimx(start_vals, fun, method = method)

# View the optimization results
print(result)

Output

               p1         p2      value     fevals  gevals   niter   convcode    kkt1
Nelder-Mead 1.999823 -3.000005 3.144259e-08 65       NA       NA        0        TRUE
              
              kkt2      xtime
Nelder-Mead   TRUE      0.009

In this example, we defined a simple quadratic function fun and used optimx() to find the minimum value of this function.

Then, we set the starting values for the optimization to (0,0) and chose the Nelder-Mead optimization method.

The optimization result is stored in the result object and can be viewed using the print() function.

The optimx also allows for many other options and methods, such as different stopping criteria, constraints, parallelization, etc.

Using the optimx with different methods and comparing the results

Let’s optimize the Rosenbrock function.

library(optimx)

rosenbrock <- function(x) {
   (1 - x[1])^2 + 100 * (x[2] - x[1]^2)^2
}

result <- optimx(c(-1.2, 1), rosenbrock,
   method = c("Nelder-Mead", "BFGS", "nlminb")
)

print(result)

Output

               p1          p2      value       fevals     gevals   niter   convcode    kkt1
Nelder-Mead  1.0002601 1.0005060 8.825241e-08   195         NA       NA        0       FALSE
BFGS         0.9998044 0.9996084 3.827383e-08   118         38       NA        0       TRUE
nlminb       1.0000000 1.0000000 2.573782e-20   44          74       35        0       TRUE
 
               kkt2     xtime
Nelder-Mead    TRUE     0.01
BFGS           TRUE     0.00
nlminb         TRUE     0.00

In this example, we used the optimx function to minimize the Rosenbrock function, a well-known test function commonly used to evaluate optimization algorithms.

The rosenbrock function is defined, which takes a vector x of length 2 and returns the value of the Rosenbrock function at that point. The Rosenbrock function has a global minimum at (1,1), with a value of 0.

In the next step, the optimx() function is called with the starting point c(-1.2, 1) and the rosenbrock function as the objective function. The method argument specifies a vector of optimization methods to be used, including “Nelder-Mead”, “BFGS”, and “nlminb”.

The optimx() function will try each method and return the result of the best optimization method. The optimization result is stored in the result object, which can be printed to the console using the print() function.

That’s it.

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