Sketchy Polytopes

Convex optimization in five easy steps

  1. Install NumPy

sudo apt-get install python-numpy

  1. Install SciPy

sudo apt-get install python-scipy

  1. Install CVXOPT

sudo apt-get install python-cvxopt

  1. Install OpenOpt
wget http://openopt.org/images/3/33/OpenOpt.zip
unzip OpenOpt.zip
cd OpenOpt
sudo python setup.py install --prefix=/usr/local/
  1. Run your second-order conic optimization program (source)

"""
OpenOpt SOCP example for the problem http://openopt.org/images/2/28/SOCP.png
"""
 
from numpy import *
from openopt import SOCP
 
f = array([-2, 1, 5])
C0 = mat('-13 3 5; -12 12 -6')
d0 = [-3, -2]
q0 = array([-12, -6, 5])
s0 = -12
 
C1 = mat('-3 6 2; 1 9 2; -1 -19 3')
d1 = [0, 3, -42]
q1 = array([-3, 6, -10])
s1 = 27
 
# you could add lb <= x <= ub, Ax <= b, Aeq x = beq constraints
# via p = SOCP(f,  ..., A=A, b=b, Aeq=Aeq, beq=beq,lb=lb, ub=ub)
p = SOCP(f,  C=[C0, C1],  d=[d0, d1], q=[q0, q1], s=[s0, s1])
r = p.solve('cvxopt_socp')
 
x_opt, f_opt = r.xf,  r.ff
 
# f_opt: -38.346368    x_opt: [-5.01428121 -5.76680444 -8.52162517]
print(' f_opt: %f    x_opt: %s' % (f_opt, x_opt))

python socp.py

------------------------- OpenOpt 0.38 -------------------------
solver: cvxopt\_socp   problem: unnamed    type: SOCP   goal: minimum
     pcost       dcost       gap    pres   dres   k/t
 0:  4.9969e+00 -1.7285e+01  6e+01  3e-01  4e+00  1e+00
 1: -1.6732e+00 -7.0431e+00  1e+01  7e-02  1e+00  6e-01
 2: -1.6221e+01 -3.5417e+01  2e+02  3e-01  5e+00  7e+00
 3: -2.1832e+01 -2.2849e+01  3e+01  4e-02  6e-01  2e+00
 4: -3.5265e+01 -3.5594e+01  1e+01  1e-02  2e-01  9e-01
 5: -3.8303e+01 -3.8314e+01  3e-01  4e-04  6e-03  2e-02
 6: -3.8342e+01 -3.8342e+01  1e-02  1e-05  2e-04  7e-04
 7: -3.8346e+01 -3.8346e+01  9e-04  1e-06  2e-05  7e-05
 8: -3.8346e+01 -3.8346e+01  4e-05  6e-08  9e-07  4e-06
 9: -3.8346e+01 -3.8346e+01  2e-06  3e-09  4e-08  2e-07
10: -3.8346e+01 -3.8346e+01  3e-07  4e-10  6e-09  3e-08
Optimal solution found.
istop: 1000 (optimal)
Solver:   Time Elapsed = 0.01     CPU Time Elapsed = 0.01
objFunValue: -38.346368
 f\_opt: -38.346368    x\_opt: \[-5.01469912 -5.76690749 -8.52177183\]
Posted by Umayr Hassan

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