transfinite | R Documentation |

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

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

`lower, upper` |
lower and upper box/bound constraints. |

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

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.

Returns to functions as components `h`

and `hinv`

of a list.

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`

.

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)

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