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I have a pretty simple Quad Program which ECOS fails to solve (Returns nan) while Gurobi / OSQP manages to solver it.
I am using CVXPY to utilize ECOS.
How to reproduce
Python code to reproduce:
# General tools
import numpy as np
import scipy as sp
# Sparse
import scipy.sparse as spa
# Solvers
import cvxpy
# Code from OSQP Benchmark
class LassoExample(object):
'''
Lasso QP example
'''
def __init__(self, n, seed=1):
# Set random seed
np.random.seed(seed)
self.n = int(n) # Number of features
self.m = int(self.n * 10) # Number of data-points
self.Ad = spa.random(self.m, self.n, density=0.15,
data_rvs=np.random.randn)
self.x_true = np.multiply((np.random.rand(self.n) >
0.5).astype(float),
np.random.randn(self.n)) / np.sqrt(self.n)
self.bd = self.Ad.dot(self.x_true) + np.random.randn(self.m)
self.lambda_max = np.linalg.norm(self.Ad.T.dot(self.bd), np.inf)
self.lambda_param = (1./5.) * self.lambda_max
self.qp_problem = self._generate_qp_problem()
def _generate_qp_problem(self):
# Construct the problem
# minimize y' * y + lambda * 1' * t
# subject to y = Ax - b
# -t <= x <= t
P = spa.block_diag((spa.csc_matrix((self.n, self.n)), 2*spa.eye(self.m), spa.csc_matrix((self.n, self.n))), format='csc')
q = np.append(np.zeros(self.m + self.n), self.lambda_param * np.ones(self.n))
In = spa.eye(self.n)
Onm = spa.csc_matrix((self.n, self.m))
A = spa.vstack([spa.hstack([self.Ad, -spa.eye(self.m),
spa.csc_matrix((self.m, self.n))]),
spa.hstack([In, Onm, -In]),
spa.hstack([In, Onm, In])]).tocsc()
l = np.hstack([self.bd, -np.inf * np.ones(self.n), np.zeros(self.n)])
u = np.hstack([self.bd, np.zeros(self.n), np.inf * np.ones(self.n)])
return P, q, A, l, u, A.shape[0], A.shape[1]
lassoQp = LassoExample(3);
P, q, A, l, u, m, n = lassoQp._generate_qp_problem();
x = cvxpy.Variable(lassoQp.n + lassoQp.m + lassoQp.n);
cvxObj = cvxpy.Minimize(cvxpy.quad_form(x, P) + (x @ q));
cvxCons = [l <= A @ x, A @ x <= u];
cvxPrblm = cvxpy.Problem(cvxObj, cvxCons);
cvxRes = cvxPrblm.solve(solver = cvxpy.ECOS, verbose = True);
I am also attaching as a .txt file SCSFail.txt (Change solver into ECOS).
Additional information
It is a LASSO problem converted into QP.
Actually SCS fails other problems from OSQP Benchmark such as: Huber Fitting, SVM.
Running the same problems with OSQP or Gurobi yields a valid solution.
Specifications
2.0.7.post1(Python PIP)Description
I have a pretty simple Quad Program which ECOS fails to solve (Returns
nan) while Gurobi / OSQP manages to solver it.I am using
CVXPYto utilizeECOS.How to reproduce
Python code to reproduce:
I am also attaching as a
.txtfile SCSFail.txt (Change solver intoECOS).Additional information
It is a LASSO problem converted into QP.
Actually SCS fails other problems from OSQP Benchmark such as: Huber Fitting, SVM.
Running the same problems with OSQP or Gurobi yields a valid solution.
Output
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