# Example_02: Hock-Schittkowski-Collection Problem 16 In ROI.plugin.deoptim: 'DEoptim' and 'DEoptimR' Plugin for the 'R' Optimization Interface

## Description

The following example solves problem 16 from the Hock-Schittkowski-Collection.

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

subject \ to: \ \ x_1 + x_2^2 ≥q 0 \ \ \ x_1^2 + x_2 ≥q 0

-2 ≥q x_1 ≥q 0.5 \ \ \ x_2 ≥q 1

Solution: `c(0.5, 0.25)`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26``` ```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 ) } 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), constraints = c(F_constraint(F=function(x) x[1] + x[2]^2, ">=", 0, J=function(x) c(1, 2*x[2])), F_constraint(F=function(x) x[1]^2 + x[2], ">=", 0, J=function(x) c(2*x[1], x[2]))), bounds = V_bound(li=1:2, ui=1:2, lb=c(-2, -Inf), ub=c(0.5, 1)) ) nlp <- ROI_solve(x, solver="deoptimr", start=c(0.4, 0.3)) nlp ## Optimal solution found. ## The objective value is: 2.499999e-01 solution(nlp) ## [1] 0.5000001 0.2499994 ```

ROI.plugin.deoptim documentation built on Aug. 30, 2020, 1:07 a.m.