In [3]:

    

from cvxpy import *

# Create two scalar optimization variables.
x = Variable()
y = Variable()

# Create two constraints.
constraints = [x + y == 1,
               x - y >= 1]

# Form objective.
obj = Minimize(square(x - y))

# Form and solve problem.
prob = Problem(obj, constraints)
prob.solve()

# The optimal dual variable (Lagrange multiplier) for
# a constraint is stored in constraint.dual_value.
print "optimal (x + y == 1) dual variable", constraints[0].dual_value
print "optimal (x - y >= 1) dual variable", constraints[1].dual_value
print "x - y value:", (x - y).value


    

    




optimal (x + y == 1) dual variable 6.47610300459e-18
optimal (x - y >= 1) dual variable 2.00025244976
x - y value: 0.999999986374

In [4]:

    

# Solving a problem with different solvers.
x = Variable(2)
obj = Minimize(norm(x, 2) + norm(x, 1))
constraints = [x >= 2]
prob = Problem(obj, constraints)

# Solve with ECOS.
prob.solve(solver=ECOS)
print "optimal value with ECOS:", prob.value

# Solve with CVXOPT.
prob.solve(solver=CVXOPT)
print "optimal value with CVXOPT:", prob.value

# Solve with SCS.
prob.solve(solver=SCS)
print "optimal value with SCS:", prob.value


    

    




optimal value with ECOS: 6.82842708233
optimal value with CVXOPT: 6.82842708994
optimal value with SCS: 6.82837896978

In [7]:

    

# Solve with ECOS.
prob.solve(solver=ECOS, verbose=True)
print "optimal value with ECOS:", prob.value


    

    




ECOS 1.0.3 - (c) A. Domahidi, Automatic Control Laboratory, ETH Zurich, 2012-2014.

It     pcost         dcost      gap     pres    dres     k/t     mu      step     IR
 0   +0.000e+00   +4.000e+00   +2e+01   2e+00   1e+00   1e+00   3e+00    N/A     1 1 -
 1   +6.451e+00   +8.125e+00   +5e+00   7e-01   5e-01   7e-01   7e-01   0.7857   1 1 1
 2   +6.788e+00   +6.839e+00   +9e-02   1e-02   8e-03   3e-02   2e-02   0.9829   1 1 1
 3   +6.828e+00   +6.829e+00   +1e-03   1e-04   8e-05   3e-04   2e-04   0.9899   1 1 1
 4   +6.828e+00   +6.828e+00   +1e-05   1e-06   8e-07   3e-06   2e-06   0.9899   2 1 1
 5   +6.828e+00   +6.828e+00   +1e-07   1e-08   8e-09   4e-08   2e-08   0.9899   2 1 1

OPTIMAL (within feastol=1.3e-08, reltol=1.5e-08, abstol=1.0e-07).
Runtime: 0.000121 seconds.

optimal value with ECOS: 6.82842708233

In [8]:

    

# Solve with SCS and display output.
opts = {"USE_INDIRECT": False}
prob.solve(solver=SCS, verbose=True, solver_specific_opts=opts)
print "optimal value with SCS:", prob.value


    

    




----------------------------------------------------------------------------
	scs v1.0 - Splitting Conic Solver
	(c) Brendan O'Donoghue, Stanford University, 2012
----------------------------------------------------------------------------
Method: sparse-direct, nnz in A = 13
EPS = 1.00e-03, ALPHA = 1.80, MAX_ITERS = 2500, NORMALIZE = 1, SCALE = 5.0
Variables n = 5, constraints m = 9
Cones:	primal zero / dual free vars: 0
	linear vars: 6
	soc vars: 3, soc blks: 1
	sd vars: 0, sd blks: 0
	exp vars: 0, dual exp vars: 0
----------------------------------------------------------------------------
 Iter | pri res | dua res | rel gap | pri obj | dua obj |  kappa  | time (s)
============================================================================
     0| 4.60e+00  5.78e-01       nan      -inf       inf  8.32e+00  1.54e-03 
    60| 3.92e-05  1.12e-04  6.64e-06  6.83e+00  6.83e+00  9.31e-18  1.62e-03 
----------------------------------------------------------------------------
Status: Solved
Timing: Solve time: 1.63e-03s, setup time: 1.70e-04s
	Lin-sys: nnz in L factor: 29, avg solve time: 1.38e-07s
	Cones: avg projection time: 5.05e-08s
----------------------------------------------------------------------------
Error metrics:
|Ax + s - b|_2 / (1 + |b|_2) = 3.9223e-05
|A'y + c|_2 / (1 + |c|_2) = 1.1168e-04
|c'x + b'y| / (1 + |c'x| + |b'y|) = 6.6446e-06
dist(s, K) = 0, dist(y, K*) = 0, s'y = 0
----------------------------------------------------------------------------
c'x = 6.8284, -b'y = 6.8285
============================================================================
optimal value with SCS: 6.82837896975

In [9]:

    

# Get ECOS arguments.
c, G, h, dims, A, b = prob.get_problem_data(ECOS)

# Get CVXOPT arguments.
c, G, h, dims, A, b = prob.get_problem_data(CVXOPT)

# Get CVXOPT arguments.
data, dims = prob.get_problem_data(SCS)


    

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