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IPOPT.R
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IPOPT.R
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.Ipopt <- new.env(parent = emptyenv())
#' Use Ipopt solver to solve optimization problems.
#'
#' \code{IPOPT} returns the solution to the optimization problem found by Ipopt solver.
#'
#' @param x Starting point
#' @param x_L Variable lower bounds
#' @param x_U Variable upper bounds
#' @param g_L Constraint lower bounds
#' @param g_U Constraint upper bounds
#' @param eval_f Callback: objective function
#' @param eval_g Callback: constraint evaluation
#' @param eval_grad_f Callback: objective function gradient
#' @param jac_g1,jac_g2 Callback: Jacobian evaluation
#' @param h1,h2 Callback: Hessian evaluation
#'
#' @return The return value will be a list which contains three components:
#' status: the status of the ipopt solver,
#' value: the optimized objective value,
#' x: the best set of parameters found.
#'
#' @examples
#' \dontrun{
#' # HS071
#' # min x1 * x4 * (x1 + x2 + x3) + x3
#' # st x1 * x2 * x3 * x4 >= 25
#' # x1^2 + x2^2 + x3^2 + x4^2 = 40
#' # 1 <= x1, x2, x3, x4 <= 5
#' # Start at (1,5,5,1)
#' # End at (1.000..., 4.743..., 3.821..., 1.379...)
#'
#' x <- c(1.0, 5.0, 5.0, 1.0)
#' x_L <- c(1.0, 1.0, 1.0, 1.0)
#' x_U <- c(5.0, 5.0, 5.0, 5.0)
#'
#' g_L <- c(25.0, 40.0)
#' g_U <- c(2.0e19, 40.0)
#'
#' eval_f <- function(x){
#' x[1] * x[4] * (x[1] + x[2] + x[3]) + x[3]
#' }
#'
#' eval_g <- function(x){
#' g = rep(0, 2)
#' g[1] = x[1] * x[2] * x[3] * x[4]
#' g[2] = x[1]^2 + x[2]^2 + x[3]^2 + x[4]^2
#' g
#' }
#'
#' eval_grad_f <- function(x){
#' grad_f = rep(0, 4)
#' grad_f[1] = x[1] * x[4] + x[4] * (x[1] + x[2] + x[3])
#' grad_f[2] = x[1] * x[4]
#' grad_f[3] = x[1] * x[4] + 1
#' grad_f[4] = x[1] * (x[1] + x[2] + x[3])
#' grad_f
#' }
#'
#' jac_g1 <- function(x){
#' rows = rep(0, 8)
#' cols = rep(0, 8)
#' rows[1] = 1; cols[1] = 1
#' rows[2] = 1; cols[2] = 2
#' rows[3] = 1; cols[3] = 3
#' rows[4] = 1; cols[4] = 4
#' # Constraint (row) 2
#' rows[5] = 2; cols[5] = 1
#' rows[6] = 2; cols[6] = 2
#' rows[7] = 2; cols[7] = 3
#' rows[8] = 2; cols[8] = 4
#' list(rows, cols)
#' }
#'
#' jac_g2 <- function(x){
#' values = rep(0, 8)
#' # Constraint (row) 1
#' values[1] = x[2]*x[3]*x[4] # 1,1
#' values[2] = x[1]*x[3]*x[4] # 1,2
#' values[3] = x[1]*x[2]*x[4] # 1,3
#' values[4] = x[1]*x[2]*x[3] # 1,4
#' # Constraint (row) 2
#' values[5] = 2*x[1] # 2,1
#' values[6] = 2*x[2] # 2,2
#' values[7] = 2*x[3] # 2,3
#' values[8] = 2*x[4] # 2,4
#' values
#' }
#'
#' h1 <- function(x){
#' # Symmetric matrix, fill the lower left triangle only
#' rows = rep(0, 10)
#' cols = rep(0, 10)
#' idx = 1
#' for (row in 1:4) {
#' for (col in 1:row) {
#' rows[idx] = row
#' cols[idx] = col
#' idx = idx + 1
#' }
#' }
#' list(rows, cols)
#' }
#'
#' h2 <- function(x, obj_factor, lambda){
#' values = rep(0, 10)
#' # Again, only lower left triangle
#' # Objective
#' values[1] = obj_factor * (2*x[4]) # 1,1
#' values[2] = obj_factor * ( x[4]) # 2,1
#' values[3] = 0 # 2,2
#' values[4] = obj_factor * ( x[4]) # 3,1
#' values[5] = 0 # 3,2
#' values[6] = 0 # 3,3
#' values[7] = obj_factor * (2*x[1] + x[2] + x[3]) # 4,1
#' values[8] = obj_factor * ( x[1]) # 4,2
#' values[9] = obj_factor * ( x[1]) # 4,3
#' values[10] = 0 # 4,4
#'
#' # First constraint
#' values[2] = values[2] + lambda[1] * (x[3] * x[4]) # 2,1
#' values[4] = values[4] + lambda[1] * (x[2] * x[4]) # 3,1
#' values[5] = values[5] + lambda[1] * (x[1] * x[4]) # 3,2
#' values[7] = values[7] + lambda[1] * (x[2] * x[3]) # 4,1
#' values[8] = values[8] + lambda[1] * (x[1] * x[3]) # 4,2
#' values[9] = values[9] + lambda[1] * (x[1] * x[2]) # 4,3
#'
#' # Second constraint
#' values[1] = values[1] + lambda[2] * 2 # 1,1
#' values[3] = values[3] + lambda[2] * 2 # 2,2
#' values[6] = values[6] + lambda[2] * 2 # 3,3
#' values[10] = values[10] + lambda[2] * 2 # 4,4
#'
#' values
#' }
#'
#' ipopt_setup()
#'
#' IPOPT(x, x_L, x_U, g_L, g_U, eval_f, eval_g, eval_grad_f, jac_g1, jac_g2, h1, h2)
#' }
#'
#' @export
IPOPT <- function(x,
x_L,
x_U,
g_L,
g_U,
eval_f,
eval_g,
eval_grad_f,
jac_g1, jac_g2,
h1, h2) {
.Ipopt$julia$call("IPOPT", x, x_L, x_U, g_L, g_U, eval_f, eval_g, eval_grad_f,
jac_g1, jac_g2, h1, h2)
}
#' Do initial setup for ipoptjlr package.
#'
#' \code{ipopt_setup} does the initial setup for ipoptjlr package.
#'
#' @param ... arguments passed to \code{JuliaCall::julia_setup}.
#'
#' @examples
#' \dontrun{
#' ipopt_setup()
#' }
#'
#' @export
ipopt_setup <- function(...) {
.Ipopt$julia <- JuliaCall::julia_setup(...)
.Ipopt$julia$install_package_if_needed("Ipopt")
.Ipopt$julia$library("Ipopt")
.Ipopt$julia$source(system.file("julia/Ipopt2.jl", package = "ipoptjlr"))
}