hs117.jl

# Hock and Schittkowski problem number 117.
#
#   Source:
#   Problem 117 in
#   W. Hock and K. Schittkowski,
#   Test examples for nonlinear programming codes,
#   Lectures Notes in Economics and Mathematical Systems 187,
#   Springer Verlag, Heidelberg, 1981.
#   
#   classification PQR-AN-15-5
#
# A. Montoison, Montreal, 05/2018.

export hs117

"HS117 model"
function hs117(args...; kwargs...)
  nlp = Model()
  x0 = 0.001 * [1, 1, 1, 1, 1, 1, 60000, 1, 1, 1, 1, 1, 1, 1, 1]
  @variable(nlp, x[i = 1:15] ≥ 0, start = x0[i])

  a = Array{Float64}(undef, 10, 5)
  a[1, :] = [-16, 2, 0, 1, 0]
  a[2, :] = [0, -2, 0, 4, 2]
  a[3, :] = [-3.5, 0, 2, 0, 0]
  a[4, :] = [0, -2, 0, -4, -1]
  a[5, :] = [0, -9, -2, 1, -2.8]
  a[6, :] = [2, 0, -4, 0, 0]
  a[7, :] = [-1, -1, -1, -1, -1]
  a[8, :] = [-1, -2, -3, -2, -1]
  a[9, :] = [1, 2, 3, 4, 5]
  a[10, :] = [1, 1, 1, 1, 1]

  b = [-40, -2, -0.25, -4, -4, -1, -40, -60, 5, 1]

  c = Float64[ 30 -20 -10  32 -10;
              -20  39 -6  -31  32;
              -10 -6   10 -6  -10;
               32 -31 -6   39 -20;
              -10  32 -10 -20  30]

  d = [4, 8, 10, 6, 2]

  e = [-15, -27, -36, -18, -12]

  for j = 1:5
    @constraint(
      nlp,
      2 * sum(c[k, j] * x[10 + k] + 3 * d[j] * x[10 + j]^2 for k = 1:5) + e[j] -
      sum(a[k, j] * x[k] for k = 1:10) ≥ 0
    )
  end

  @objective(
    nlp,
    Min,
    -sum(b[j] * x[j] for j = 1:10) +
    sum(sum(c[k, j] * x[10 + k] * x[10 + j] for k = 1:5) for j = 1:5) +
    2 * sum(d[j] * x[10 + j]^3 for j = 1:5)
  )

  return nlp
end