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## Optimization test function GENROSE
rm(list = ls())
library(optimx)
genrose.f <- function(x, gs = NULL) {
# objective function
## One generalization of the Rosenbrock banana valley
# function (n parameters)
n <- length(x)
if (is.null(gs)) {
gs = 100
}
fval <- 1 + sum(gs * (x[1:(n - 1)]^2 - x[2:n])^2 + (x[2:n] -
1)^2)
return(fval)
}
genrose.h <- function(x, gs = NULL) {
## compute Hessian
if (is.null(gs)) {
gs = 100
}
n <- length(x)
hh <- matrix(rep(0, n * n), n, n)
for (i in 2:n) {
z1 <- x[i] - x[i - 1] * x[i - 1]
z2 <- 1 - x[i]
hh[i, i] <- hh[i, i] + 2 * (gs + 1)
hh[i - 1, i - 1] <- hh[i - 1, i - 1] - 4 * gs * z1 -
4 * gs * x[i - 1] * (-2 * x[i - 1])
hh[i, i - 1] <- hh[i, i - 1] - 4 * gs * x[i - 1]
hh[i - 1, i] <- hh[i - 1, i] - 4 * gs * x[i - 1]
}
return(hh)
}
genrose.g <- function(x, gs = NULL) {
# vectorized gradient for genrose.f
# Ravi Varadhan 2009-04-03
n <- length(x)
if (is.null(gs)) {
gs = 100
}
gg <- as.vector(rep(0, n))
tn <- 2:n
tn1 <- tn - 1
z1 <- x[tn] - x[tn1]^2
z2 <- 1 - x[tn]
gg[tn] <- 2 * (gs * z1 - z2)
gg[tn1] <- gg[tn1] - 4 * gs * x[tn1] * z1
gg
}
xx <- rep(2, 6)
g6o <- opm(xx, genrose.f, genrose.g, method="MOST", gs = 100)
print(summary(g6o, order=value))
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