Example-1 {ROI.plugin.deoptim}

Banana

Description

The following example is also known as Rosenbrock's banana function (https://en.wikipedia.org/wiki/Rosenbrock_function).

minimize \ f(x) = 100 (x_2 - x_1^2)^2 + (1 - x_1)^2

Solution: c(1, 1)

Examples

Sys.setenv(ROI_LOAD_PLUGINS = FALSE)
library(ROI)
library(ROI.plugin.deoptim)


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

x <- OP( objective = F_objective(f, n=2L, names=c("x_1", "x_2")), 
         bounds = V_bound(li=1:2, ui=1:2, lb=c(-3, -3), ub=c(3,  3)) )

nlp <- ROI_solve(x, solver = "deoptim")
nlp
## Optimal solution found.
## The objective value is: 3.828383e-22
solution(nlp)
## x_1 x_2 
##   1   1