Try our new documentation site (beta).


Source code for the experiment of optimizing over a circle


from gurobipy import *
from math import *
import random
import time
import sys

# Work on a circle defined on a million constraints
t0      = time.time()
n       = 1024 * 1024
m       = Model('Circle Optimization')
X       = m.addVars(2,lb=-2,ub=2)
Wb      = 0
Wc      = 0
Wd      = 0
maxdiff = 0
niter   = 0
margin  = 1.01

m.addConstrs(X[0]*cos((2*pi*i)/n) + X[1]*sin((2*pi*i)/n) <= 1
             for i in range(n))
print('Added 2 Vars and %d constraints in %.2f seconds' %
      (n, time.time()-t0))
m.Params.OutputFlag = 0
m.Params.Presolve   = 0

# Now select random objectives and optimize. Resulting optimal
# solution must be in the circle
for i in range(4096):
  theta=2*pi*random.random()
  a = cos(theta)
  b = sin(theta)
  m.setObjective(X[0] * a + X[1] * b)
  m.optimize()
  niter  += m.IterCount

  # See how far is the solution from the boundary of a circle of
  # radius one, if we minimize (a,b) the optimal solution should be (-a,-b)
  error  = (X[0].X+a)*(X[0].X+a) + (X[1].X+b)*(X[1].X+b)

  # Display most inacurate solution
  if (error > margin * maxdiff  or
      m.BoundVio > margin * Wb  or
      m.ConstrVio > margin * Wc or
      m.DualVio > margin * Wd     ):
    maxdiff = max(maxdiff, error)
    Wb      = max(Wb, m.BoundVio)
    Wc      = max(Wb, m.ConstrVio)
    Wd      = max(Wd, m.DualVio)
    print('Errors: %g %g %g %g Iter %d %d Kappa %g' %
          (maxdiff, Wb, Wc, Wd, i, niter, m.KappaExact))
    sys.stdout.flush()

Try Gurobi for Free

Choose the evaluation license that fits you best, and start working with our Expert Team for technical guidance and support.

Evaluation License
Get a free, full-featured license of the Gurobi Optimizer to experience the performance, support, benchmarking and tuning services we provide as part of our product offering.
Academic License
Gurobi supports the teaching and use of optimization within academic institutions. We offer free, full-featured copies of Gurobi for use in class, and for research.
Cloud Trial

Request free trial hours, so you can see how quickly and easily a model can be solved on the cloud.

Search

Gurobi Optimization