basic cvxopt linear programming

basic_lp.py

import numpy as np
from cvxopt import matrix, printing, solvers

# configuration - turn down the volume and set output formatting
solvers.options['show_progress'] = False
solvers.options['LPX_K_MSGLEV'] = 0
printing.options['dformat'] = '% .3f'


# MINIMIZE - portfolio of current bond prices
p = matrix([109,94.8,99.5,93.1,97.2,92.9,110,104,102,95.2], tc='d')

# CONSTRAINT - bond cash flows
c = np.array([[ 10,  7,  8,  6,  7,  5, 10,  8,  7,100],
              [ 10,  7,  8,  6,  7,  5, 10,  8,107,  0],
              [ 10,  7,  8,  6,  7,  5,110,108,  0,  0],
              [ 10,  7,  8,  6,  7,105,  0,  0,  0,  0],
              [ 10,  7,  8,106,107,  0,  0,  0,  0,  0],
              [110,107,108,  0,  0,  0,  0,  0,  0,  0]])
I = np.eye(10)  # non-negative portfolio weights
c = matrix(np.vstack([c, I]), tc='d')

# CONSTRAINT - obligations
o = np.array([100,200,800,100,800,1200])
o = matrix(np.hstack([o, np.zeros(10)]), tc='d')


# cvxopt solution
#soln = solvers.lp(p, -c, -o)
soln = solvers.lp(p, -c, -o, solver='glpk')

c = 0
for i in soln['x']:
    print 'x{0:d} = {1:6.3f}'.format(c,i)
    c += 1
print '\nminimum portfolio cost: ${0:,.2f}'.format((p.T*soln['x'])[0])

results.txt

x0 =  0.000
x1 = 11.215
x2 =  0.000
x3 =  6.807
x4 =  0.000
x5 =  0.000
x6 =  0.000
x7 =  6.302
x8 =  0.283
x9 =  0.000

minimum portfolio cost: $2,381.14