tquartic.jl

#   A quartic function with nontrivial groups and
#   repetitious elements.

#   Source:
#   Ph. Toint, private communication.

#   classification SUR2-AN-V-0#

#   Problem 57 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 tquartic

"A quartic function with nontrivial groups and repetitious elements in size 'n' "
function tquartic(args...; n::Int = default_nvar, kwargs...)
  n < 2 && @warn("tquartic: number of variables must be ≥ 2")
  n = max(2, n)

  nlp = Model()

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

  @NLobjective(
    nlp,
    Min,
    0.5 * (x[1] - 1.0)^2 + 0.5 * sum((x[1]^2 - x[i + 1]^2)^2 for i = 1:(n - 2))
  )

  return nlp
end