#!/bin/env python
# Solve a simple quadratic optimization problem. Given a matrix
# Q and a point x0, minimize the quadratic function
#
# x' (Q + alpha I) x
#
# subject to the linear system Q (x - x0) = 1 and nonnegativity on all
# variables. Report solution if available
from __future__ import print_function
import xpress as xp
import numpy as np
N = 10
Q = np.arange (1,N**2 + 1).reshape (N, N)
x = np.array ([xp.var () for i in range (N)])
x0 = np.random.random (N)
p = xp.problem()
p.addVariable (x)
# c1 and c2 are two systems of constraints of size N each written as
#
# (x-x0)' Q = 1
#
# Qx >= 0
c1 = - xp.Dot ((x - x0), Q) == 1
c2 = xp.Dot (Q, x) >= 0
# The objective function is quadratic:
p.addConstraint (c1,c2)
p.setObjective (xp.Dot (x, Q + N**3 * np.eye (N), x))
p.solve("")
print ("nrows, ncols:", p.attributes.rows, p.attributes.cols)
print ("solution:", p.getSolution ())
p.write ("test5-qp", "lp")
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