#Rosenbrock banana valley function
f <- function(x){
return(100*(x[2] - x[1]*x[1])^2 + (1-x[1])^2)
}
#gradient
gr <- function(x){
return(c(-400*x[1]*(x[2] - x[1]*x[1]) - 2*(1-x[1]), 200*(x[2] - x[1]*x[1])))
}
#Hessian
h <- function(x) {
a11 <- 2 - 400*x[2] + 1200*x[1]*x[1]; a21 <- -400*x[1]
return(matrix(c(a11, a21, a21, 200), 2, 2))
}
fg <- function(x){ #function and gradient
val <- f(x)
attr(val,"gradient") <- gr(x)
val
}
fgh <- function(x){ #function and gradient
val <- f(x)
attr(val,"gradient") <- gr(x)
attr(val,"hessian") <- h(x)
val
}
x0 <- c(-1.2, 1)
sr <- snewton(x0, fn=f, gr=gr, hess=h, control=list(trace=1))
print(sr)
# Call through optimr to get correct calling sequence, esp. with bounds
srm <- optimr(x0, fn=f, gr=gr, hess=h, control=list(trace=1))
print(srm)
# bounds constrained example
lo <- rep((min(x0)-0.1), 2)
up <- rep((max(x0)+0.1), 2)
# Call through optimr to get correct calling sequence, esp. with bounds
srmb <- optimr(x0, fn=f, gr=gr, hess=h, lower=lo, upper=up, control=list(trace=1))
proptimr(srmb)
#Example 2: Wood function
#
wood.f <- function(x){
res <- 100*(x[1]^2-x[2])^2+(1-x[1])^2+90*(x[3]^2-x[4])^2+(1-x[3])^2+
10.1*((1-x[2])^2+(1-x[4])^2)+19.8*(1-x[2])*(1-x[4])
return(res)
}
#gradient:
wood.g <- function(x){
g1 <- 400*x[1]^3-400*x[1]*x[2]+2*x[1]-2
g2 <- -200*x[1]^2+220.2*x[2]+19.8*x[4]-40
g3 <- 360*x[3]^3-360*x[3]*x[4]+2*x[3]-2
g4 <- -180*x[3]^2+200.2*x[4]+19.8*x[2]-40
return(c(g1,g2,g3,g4))
}
#hessian:
wood.h <- function(x){
h11 <- 1200*x[1]^2-400*x[2]+2; h12 <- -400*x[1]; h13 <- h14 <- 0
h22 <- 220.2; h23 <- 0; h24 <- 19.8
h33 <- 1080*x[3]^2-360*x[4]+2; h34 <- -360*x[3]
h44 <- 200.2
H <- matrix(c(h11,h12,h13,h14,h12,h22,h23,h24,
h13,h23,h33,h34,h14,h24,h34,h44),ncol=4)
return(H)
}
#################################################
w0 <- c(-3, -1, -3, -1)
wd <- snewton(w0, fn=wood.f, gr=wood.g, hess=wood.h, control=list(trace=1))
print(wd)
# Call through optimr to get correct calling sequence, esp. with bounds
wdm <- optimr(w0, fn=wood.f, gr=wood.g, hess=wood.h, control=list(trace=1))
print(wdm)
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