palmer7c.jl

#   A linear least squares problem
#   arising from chemical kinetics.
#
#   model: H-N=C=Se TZVP+MP2
#   fitting Y to A0 + A2 X**2 + A4 X**4 + A6 X**6 + A8 X**8 +
#                A10 X**10 + A12 X**12 + A14 X**14
#
#   Source:
#   M. Palmer, Edinburgh, private communication.
#
#   classification QUR2-RN-8-0

export palmer7c

"A linear least squares problem arising from chemical kinetics."
function palmer7c(args...; kwargs...)
  nlp = Model()

  @variable(nlp, x[j = 1:8], start = 1.0)

  X = [
    0.000000,
    0.139626,
    0.261799,
    0.436332,
    0.565245,
    0.512942,
    0.610865,
    0.785398,
    0.959931,
    1.134464,
    1.308997,
    1.483530,
    1.658063,
  ]

  Y = [
    4.419446,
    3.564931,
    2.139067,
    0.404686,
    0.000000,
    0.035152,
    0.146813,
    2.718058,
    9.474417,
    26.132221,
    41.451561,
    72.283164,
    117.630959,
  ]

  @NLobjective(
    nlp,
    Min,
    0.5 * sum((Y[i] - sum(x[j] * X[i]^(2 * j - 2) for j = 1:8))^2 for i = 1:13)
  )

  return nlp
end