palmer5d.jl

#   A linear least squares problem
#   arising from chemical kinetics.
#
#   model: H-N=C=Se TZVP+MP2
#   fitting Y to to A0 + A2 X**2 + A4 X**4 + A6 X**6
#
#   Source:
#   M. Palmer, Edinburgh, private communication.
#
#   classification QUR2-RN-4-0

export palmer5d

"A linear least squares problem arising from chemical kinetics."
function palmer5d(args...; kwargs...)
  nlp = Model()

  @variable(nlp, x[j = 1:4], start = 1.0)

  X = [
    0.000000,
    1.570796,
    1.396263,
    1.308997,
    1.221730,
    1.125835,
    1.047198,
    0.872665,
    0.698132,
    0.523599,
    0.349066,
    0.174533,
  ]

  Y = [
    83.57418,
    81.007654,
    18.983286,
    8.051067,
    2.044762,
    0.000000,
    1.170451,
    10.479881,
    25.785001,
    44.126844,
    62.822177,
    77.719674,
  ]

  @NLobjective(
    nlp,
    Min,
    0.5 * sum((Y[i] - sum(x[j] * X[i]^(2 * j - 2) for j = 1:4))^2 for i = 1:12)
  )

  return nlp
end