sosdemo6.jl

# Adapted from:
# SOSDEMO6 --- MAX CUT
# Section 3.6 of SOSTOOLS User's Manual

@testset "SOSDEMO6 with $solver" for solver in sdp_solvers
  @polyvar x[1:5]

  # Number of cuts
  f = 2.5 - 0.5*x[1]*x[2] - 0.5*x[2]*x[3] - 0.5*x[3]*x[4] - 0.5*x[4]*x[5] - 0.5*x[5]*x[1]

  # Boolean constraints
  bc = x.^2 - 1

  for (gamma, expected) in [(3.9, :Infeasible), (4, :Optimal)]

    m = SOSModel(solver = solver)

    Z = monomials(x, 0:1)
    @variable m p1 >= 0 Poly{true}(Z)

    Z = monomials(x, 0:2)
    @variable m p[1:5] Poly(Z)

    @constraint m p1*(gamma-f) + dot(p, bc) >= (gamma-f)^2

    status = solve(m)

    @test status == expected
  end
end