# transfinite: Boxed Region Transformation In adagio: Discrete and Global Optimization Routines

## Description

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

## Usage

 `1` ```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.

## 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, `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.

## Value

Returns to functions as components `h` and `hinv` of a list.

## Note

Based on an idea of Ravi Varadhan, intrinsically used in his implementation of Nelder-Mead in the ‘dfoptim’ package.

For positivity constraints, `x>=0`, this approach is considered to be numerically more stable than `x-->exp(x)` or `x-->x^2`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```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 ## End(Not run) ```

adagio documentation built on May 29, 2017, 10:29 p.m.