Nothing
## ----setSweaveOptions,echo=FALSE--------------------------
# have an (invisible) initialization noweb chunk
# to remove the default continuation prompt ">"
options(continue = " ")
options(width = 60)
# eliminate margin space above plots
options(SweaveHooks = list(fig = function() par(mar = c(5.1, 4.1, 1.1, 2.1))))
## ----installNLopt, eval=FALSE-----------------------------
# install.packages("nloptr")
## ----installNLoptSource, eval=FALSE-----------------------
# install.packages("nloptr", type = "source")
## ----testNLoptInstallation, eval=FALSE--------------------
# library("nloptr")
# ?nloptr
## ----installNLoptGithub, eval=FALSE-----------------------
# # install.packages("remotes")
# remotes::install_github("astamm/nloptr")
## ----loadLibrary------------------------------------------
library(nloptr)
## ----defineRosenbrockBanana-------------------------------
## Rosenbrock Banana function
eval_f <- function(x) {
100 * (x[2] - x[1] * x[1]) ^ 2 + (1 - x[1]) ^ 2
}
## Gradient of Rosenbrock Banana function
eval_grad_f <- function(x) {
c(-400 * x[1] * (x[2] - x[1] * x[1]) - 2 * (1 - x[1]),
200 * (x[2] - x[1] * x[1]))
}
## ----setRosenbrockBananaInitialValues---------------------
# initial values
x0 <- c(-1.2, 1)
## ----setRosenbrockBananaOptions---------------------------
opts <- list("algorithm" = "NLOPT_LD_LBFGS",
"xtol_rel" = 1.0e-8)
## ----solveRosenbrockBanana--------------------------------
# solve Rosenbrock Banana function
res <- nloptr(x0 = x0,
eval_f = eval_f,
eval_grad_f = eval_grad_f,
opts = opts)
## ----printRosenbrockBanana--------------------------------
print(res)
## ----defineRosenbrockBananaList---------------------------
## Rosenbrock Banana function and gradient in one function
eval_f_list <- function(x) {
common_term <- x[2] - x[1] * x[1]
list("objective" = 100 * common_term ^ 2 + (1 - x[1]) ^ 2,
"gradient" = c(-400 * x[1] * common_term - 2 * (1 - x[1]),
200 * common_term))
}
## ----solveRosenbrockBananaList----------------------------
res <- nloptr(x0 = x0,
eval_f = eval_f_list,
opts = opts)
print(res)
## ----defineTutorialObjective------------------------------
# objective function
eval_f0 <- function(x, a, b) {
sqrt(x[2])
}
# gradient of objective function
eval_grad_f0 <- function(x, a, b) {
c(0, 0.5 / sqrt(x[2]))
}
## ----defineTutorialConstraints----------------------------
# constraint function
eval_g0 <- function(x, a, b) {
(a * x[1] + b) ^ 3 - x[2]
}
# Jacobian of constraint
eval_jac_g0 <- function(x, a, b) {
rbind(c(3 * a[1] * (a[1] * x[1] + b[1]) ^ 2, -1.0),
c(3 * a[2] * (a[2] * x[1] + b[2]) ^ 2, -1.0))
}
## ----defineTutorialParameters-----------------------------
# define parameters
a <- c(2, -1)
b <- c(0, 1)
## ----solveTutorialWithGradient----------------------------
# Solve using NLOPT_LD_MMA with gradient information supplied in separate
# function
res0 <- nloptr(x0 = c(1.234, 5.678),
eval_f = eval_f0,
eval_grad_f = eval_grad_f0,
lb = c(-Inf, 0),
ub = c(Inf, Inf),
eval_g_ineq = eval_g0,
eval_jac_g_ineq = eval_jac_g0,
opts = list("algorithm" = "NLOPT_LD_MMA",
"xtol_rel" = 1.0e-8,
"print_level" = 2,
"check_derivatives" = TRUE,
"check_derivatives_print" = "all"),
a = a,
b = b)
print(res0)
## ----solveTutorialWithoutGradient-------------------------
# Solve using NLOPT_LN_COBYLA without gradient information
res1 <- nloptr(x0 = c(1.234, 5.678),
eval_f = eval_f0,
lb = c(-Inf, 0),
ub = c(Inf, Inf),
eval_g_ineq = eval_g0,
opts = list("algorithm" = "NLOPT_LN_COBYLA",
"xtol_rel" = 1.0e-8),
a = a,
b = b)
print(res1)
## ----derivativeCheckerDefineFunctions---------------------
g <- function(x, a) {
c(x[1] - a[1],
x[2] - a[2],
(x[1] - a[1]) ^ 2,
(x[2] - a[2]) ^ 2,
(x[1] - a[1]) ^ 3,
(x[2] - a[2]) ^ 3)
}
g_grad <- function(x, a) {
rbind(
c(1, 0),
c(0, 1),
c(2 * (x[1] - a[1]), 0),
c(2 * (x[1] - a[1]), 2 * (x[2] - a[2])),
c(3 * (x[1] - a[2]) ^ 2, 0),
c(0, 3 * (x[2] - a[2]) ^ 2)
)
}
## ----derivativeCheckerPrint-------------------------------
res <- check.derivatives(
.x = c(1, 2),
func = g,
func_grad = g_grad,
check_derivatives_print = "all",
a = c(0.3, 0.8)
)
## ----derivativeCheckerResult------------------------------
res
## ----printAllOptions--------------------------------------
nloptr::nloptr.print.options()
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