import numpy as np
import scipy.sparse as spa
import cvxpy
class RandomQPExample(object):
'''
Random QP example
'''
def __init__(self, n, seed=1):
'''
Generate problem in QP format and CVXPY format
'''
# Set random seed
np.random.seed(seed)
m = int(n * 10)
# Generate problem data
self.n = int(n)
self.m = m
P = spa.random(n, n, density=0.15,
data_rvs=np.random.randn,
format='csc')
self.P = P.dot(P.T).tocsc() + 1e-02 * spa.eye(n)
self.q = np.random.randn(n)
self.A = spa.random(m, n, density=0.15,
data_rvs=np.random.randn,
format='csc')
v = np.random.randn(n) # Fictitious solution
delta = np.random.rand(m) # To get inequality
self.u = self.A@v + delta
self.l = - np.inf * np.ones(m) # self.u - np.random.rand(m)
self.qp_problem = self._generate_qp_problem()
self.cvxpy_problem = self._generate_cvxpy_problem()
@staticmethod
def name():
return 'Random QP'
def _generate_qp_problem(self):
'''
Generate QP problem
'''
problem = {}
problem['P'] = self.P
problem['q'] = self.q
problem['A'] = self.A
problem['l'] = self.l
problem['u'] = self.u
problem['m'] = self.A.shape[0]
problem['n'] = self.A.shape[1]
return problem
def _generate_cvxpy_problem(self):
'''
Generate QP problem
'''
x_var = cvxpy.Variable(self.n)
objective = .5 * cvxpy.quad_form(x_var, self.P) + self.q * x_var
constraints = [self.A * x_var <= self.u, self.A * x_var >= self.l]
problem = cvxpy.Problem(cvxpy.Minimize(objective), constraints)
return problem
def revert_cvxpy_solution(self):
'''
Get QP primal and duar variables from cvxpy solution
'''
variables = self.cvxpy_problem.variables()
constraints = self.cvxpy_problem.constraints
# primal solution
x = variables[0].value
# dual solution
y = constraints[0].dual_value - constraints[1].dual_value
return x, y
