Example-1 {ROI.plugin.alabama} | R Documentation |
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)
library(ROI) f <- function(x) { return( 100 * (x[2] - x[1]^2)^2 + (1 - x[1])^2 ) } f.gradient <- function(x) { return( c( -400 * x[1] * (x[2] - x[1] * x[1]) - 2 * (1 - x[1]), 200 * (x[2] - x[1] * x[1])) ) } x <- OP(objective = F_objective(f, n = 2L, G = f.gradient), bounds = V_bound(li = 1:2, ui = 1:2, lb = c(-3, -3), ub = c(3, 3))) nlp <- ROI_solve(x, solver = "alabama", start = c(-2, 2.4), method = "BFGS") nlp ## Optimal solution found. ## The objective value is: 3.049556e-23 solution(nlp) ## [1] 1 1