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Transformation of a box/bound constrained region to an unconstrained one.
transfinite(lower, upper, n = length(lower))lower and upper box/bound constraints.
length of upper, lower if both are scalars, to which they get repeated.
Returns to functions as components h and hinv of a list.
Transforms a constraint region in n-dimensional space bijectively to the
unconstrained atanh resp. exp
transformation to each single variable that is bound constraint.
It provides two functions, h: B = []x...x[] --> R^n and its inverse
hinv. These functions can, for example, be used to add box/bound
constraints to a constrained optimization problem that is to be solved with
a (nonlinear) solver not allowing constraints.
# NOT RUN {
lower <- c(-Inf, 0, 0)
upper <- c( Inf, 0.5, 1)
Tf <- transfinite(lower, upper)
h <- Tf$h; hinv <- Tf$hinv
# }
# NOT RUN {
## Solve Rosenbrock with one variable restricted
rosen <- function(x) {
n <- length(x)
x1 <- x[2:n]; x2 <- x[1:(n-1)]
sum(100*(x1-x2^2)^2 + (1-x2)^2)
}
f <- function(x) rosen(hinv(x)) # f must be defined on all of R^n
x0 <- c(0.1, 0.1, 0.1) # starting point not on the boundary!
nm <- nelder_mead(h(x0), f) # unconstraint Nelder-Mead
hinv(nm$xmin); nm$fmin # box/bound constraint solution
# [1] 0.7085596 0.5000000 0.2500004
# [1] 0.3353605
# }
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