pracma (version 1.2.0)

transfinite: Boxed Region Transformation

Description

Transformation of a box/bound constrained region to an unconstrained one.

Usage

transfinite(lower, upper, n = length(lower))

Arguments

lower, upper

lower and upper box/bound constraints.

n

length of upper, lower if both are scalars, to which they get repeated.

Value

• Returns to functions as components g and ginv of a list.

Details

Transforms a constraint region in n-dimensional space bijectively to the unconstrained $R^n$ space, applying a atanh resp. exp transformation to each single variable that is bound constraint.

It provides two functions, g: []x...x[] --> R^n and its inverse ginv. 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.

Examples

lower <- c(-Inf, 0,   0)
upper <- c( Inf, 0.5, 1)
Tf <- transfinite(lower, upper)
g <- Tf$g; h <- Tf$ginv

##  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(h(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(g(x0), f)     # unconstraint Nelder-Mead
h(nm$xmin); nm$fmin             # box/bound constraint solution
# [1] 0.7085596 0.5000000 0.2500004
# [1] 0.3353605