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#' El-Attar-Vidyasagar-Dutta Function
#'
#' This function is based on the formula
#' \deqn{f(\mathbf{x}) = (\mathbf{x}_1^2 + \mathbf{x}_2 - 10)^2 + (\mathbf{x}_1 + \mathbf{x}_2^2 - 7)^2 + (\mathbf{x}_1^2 + \mathbf{x}_2^3 - 1)^2}
#' subject to \eqn{\mathbf{x}_i \in [-500, 500], i = 1, 2}.
#'
#' @references R. A. El-Attar, M. Vidyasagar, S. R. K. Dutta, An Algorithm for
#' II-norm Minimiza- tion With Application to Nonlinear II-approximation, SIAM
#' Journal on Numverical Analysis, vol. 16, no. 1, pp. 70-86, 1979.
#'
#' @template ret_smoof_single
#' @export
makeElAttarVidyasagarDuttaFunction = function() {
makeSingleObjectiveFunction(
name = "El-Attar-Vidyasagar-Dutta Function",
id = "elAttarVidyasagarDutta_2d",
fn = function(x) {
assertNumeric(x, len = 2L, any.missing = FALSE, all.missing = FALSE)
(x[1]^2 + x[2] - 10)^2 + (x[1] + x[2]^2 - 7)^2 + (x[1]^2 + x[2]^3 - 1)^2
},
par.set = makeNumericParamSet(
len = 2L,
id = "x",
lower = c(-100, -100),
upper = c(100, 100),
vector = TRUE
),
tags = attr(makeElAttarVidyasagarDuttaFunction, "tags"),
global.opt.params = c(3.40918683, -2.17143304),
global.opt.value = 1.712780354
)
}
class(makeElAttarVidyasagarDuttaFunction) = c("function", "smoof_generator")
attr(makeElAttarVidyasagarDuttaFunction, "name") = c("El-Attar-Vidyasagar-Dutta")
attr(makeElAttarVidyasagarDuttaFunction, "type") = c("single-objective")
attr(makeElAttarVidyasagarDuttaFunction, "tags") = c("single-objective", "continuous", "differentiable", "non-separable", "non-scalable", "unimodal")
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