Solving a nonconvex quadratic problem

# Test problem on a dot product between matrices of scalars and/or of
# variables. Note that the problem cannot be solved by the Optimizer
# as it is nonconvex.
#
# (C) Fair Isaac Corp., 1983-2025

import xpress as xp
import numpy as np

a = 0.1 + np.arange(21).reshape(3, 7)

p = xp.problem()

# Create NumPy vectors of variables
y = p.addVariables(3, 7, name='')
x = p.addVariables(7, 5, name='')

p.addConstraint(xp.Dot(y, x) <= 0)
p.addConstraint(xp.Dot(a, x) == 1)

p.setObjective(x[0][0])

p.optimize()

# Turns out the problem is infeasible, so let's use nonlinear IIS using the global solver to find out why

# Find the first IIS and stop once it is found
p.iisfirst(0)

miisrow = []
miiscol = []
constrainttype = []
colbndtype = []
duals = []
rdcs = []
isolationrows = []
isolationcols = []

# get data for the IIS
p.getiisdata(1, miisrow, miiscol, constrainttype, colbndtype,
                duals, rdcs, isolationrows, isolationcols)

#print the IIS
print("iis data:", miisrow, miiscol, constrainttype, colbndtype,
      duals, rdcs, isolationrows, isolationcols)