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hs117.jl
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hs117.jl
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# 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 = Array{Float64}(undef, 5, 5)
c[1, :] = [30, -20, -10, 32, -10]
c[2, :] = [-20, 39, -6, -31, 32]
c[3, :] = [-10, -6, 10, -6, -10]
c[4, :] = [32, -31, -6, 39, -20]
c[5, :] = [-10, 32, -10, -20, 30]
d = [4, 8, 10, 6, 2]
e = [-15, -27, -36, -18, -12]
for j = 1:5
@NLconstraint(
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
@NLobjective(
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