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

# 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

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

# 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

# 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)