sinquad.jl

#   Another function with nontrivial groups and
#   repetitious elements.

#   Source:
#   N. Gould, private communication.

#   classification OUR2-AY-V-0

#   Problem 51 in
#   L. Luksan, C. Matonoha and J. Vlcek
#   Modified CUTE problems for sparse unconstrained optimization,
#   Technical Report 1081,
#   Institute of Computer Science,
#   Academy of Science of the Czech Republic
#   http://www.cs.cas.cz/matonoha/download/V1081.pdf
#
# J.-P. Dussault, Clermont-Ferrand 05/2016.

export sinquad

"Another function with nontrivial groups and repetitious elements in size 'n' "
function sinquad(args...; n::Int = default_nvar, kwargs...)
  n < 3 && @warn("sinquad: number of variables must be ≥ 3")
  n = max(3, n)

  nlp = Model()

  @variable(nlp, x[i = 1:n], start = 0.1)

  @NLobjective(
    nlp,
    Min,
    (x[1] - 1.0)^4 +
    (x[n]^2 - x[1]^2)^2 +
    sum((sin(x[i] - x[n]) - x[1]^2 + x[i]^2)^2 for i = 2:(n - 1))
  )

  return nlp
end