Hi,
thanks for the great forum first of all. I am fairly new to the use of OSQP, so I fear this could be a duplicate of another question or something obvious, but I could not find an answer to my problem until now…
I am working on a simple problem of the form
min 1/2*x’Px
s.t. Ax=b
lb<=x<=ub
I have three implementations of the problem: one in Python, and 2 in Matlab (in the first, I have defined P and A_eq to be sparse, in the second they are just normal Matlab matrices).
To ensure reproducibility of the optimal solution found, I have set adaptive_rho_interval=50 (as suggested in other posts like this one).
However,I observe that:
- the solution obtained in Python is exactly the same as the one found in Matlab without the use of the sparse matrices
- the solution found in Matlab using the sparse matrices is different.
Is there any reason for this to be happening?
I copy my two scripts in the following, to reproduce the issue. To make the code more readable, I specify the values of the vectors/matrices used at the bottom of the question.
Thank you very much in advance.
Matlab code:
w = [ones(1,33), 0.01*ones(1,8), 10*ones(1,9)];
lb = [zeros(1,33), -6*ones(1,17)];
ub = [ones(1,33), 6*ones(1,17)];
%% use OSQP without sparse matrices
% rewrite the cost function as x'Px
P = diag(2*w);
prob = osqp;
A_eq_osqp = [A_eq; eye(50)];
lb_osqp = [B_eq; lb'];
ub_osqp = [B_eq; ub'];
% Setup workspace
prob.setup(P, [], A_eq_osqp, lb_osqp, ub_osqp, 'verbose', 0, 'adaptive_rho_interval', 50);
% Solve problem
res = prob.solve();
x_osqp = res.x;
%% then use OSQP with sparse matrixes
% rewrite the cost function as x'Px
P = sparse(diag(2*w));
prob = osqp;
A_eq_osqp = sparse([A_eq; eye(50)]);
lb_osqp = [B_eq; lb'];
ub_osqp = [B_eq; ub'];
% Setup workspace
prob.setup(P, [], A_eq_osqp, lb_osqp, ub_osqp, 'verbose', 0, 'adaptive_rho_interval', '50');
% Solve problem
res_sparse = prob.solve();
x_osqp_sparse = res_sparse.x;
%% Plot the comparison
h = figure;
set(gca,'fontsize',15,'LineWidth',2)
hold on
plot(x_osqp, 'LineWidth',2)
plot(x_osqp_sparse, 'LineWidth',2)
legend( "OSQP","OSQP sparse")
xlabel("optimization variables")
grid on
Python code:
import numpy as np
import osqp
from scipy import sparse
lb = np.concatenate((np.zeros((1, 33)), -6*np.ones((1, 17))), axis=1)
ub = np.concatenate((np.ones((1, 33)), 6*np.ones((1, 17))), axis=1)
## SOLVE with OSQP
w = np.concatenate((np.ones((1, 33)), 0.01*np.ones((1, 8)), 10*np.ones((1, 9))), axis=1)
P = sparse.csc_matrix(2*np.diagflat(w))
A_eq_osqp = sparse.csc_matrix(np.concatenate((A_eq, np.eye(50)), axis=0))
lb_osqp = np.concatenate((np.transpose(np.atleast_2d(B_eq)), np.transpose(lb)), axis=0)
ub_osqp = np.concatenate((np.transpose(np.atleast_2d(B_eq)), np.transpose(ub)), axis=0)
prob = osqp.OSQP()
prob.setup(P=P, A=A_eq_osqp, l=lb_osqp, u=ub_osqp, verbose=False, adaptive_rho_interval=50)
res = prob.solve()
x_opt = res.x
Matrices (in Python format):
B_eq = np.array([-4.18274179e+00, 1.56056756e+01, -1.67703208e+00, 2.02253004e+00,
1.02790865e+01, -2.01405712e+00, -3.32916514e+02, -1.75742282e+02,
1.15009521e+02, 4.65990026e+01, 1.47867987e+03, -2.88275491e+02,
-3.45840577e+03, -1.02597422e+03, 3.26288535e+03, 2.15487771e+02,
4.83631402e+02])
A_eq = np.array([[ 5.59696010e+01, 1.50303950e+02, -1.45080962e+01,
2.42435057e+01, -3.82537529e+01, -1.74936497e+01,
-1.67269744e+01, 3.02613145e+01, 4.94917744e+01,
3.89645168e+01, 7.09048417e+00, 5.96168902e-01,
-3.68276595e+01, 6.75212395e+00, -3.33314640e+00,
-1.14602731e+01, -2.54238971e+00, 7.14121399e+00,
-6.43876344e+01, -2.35359455e+01, -1.96299142e+01,
-5.77662614e+01, -4.17765699e+01, -5.76682147e+01,
-2.15573061e+01, 2.54067375e+01, 2.92530478e+01,
2.91631734e+01, 1.14630510e+00, 1.51251526e+01,
-3.23904168e+01, 1.25577904e+01, 1.32951586e+01,
0.00000000e+00, 8.16171599e+00, 3.78787898e-01,
6.93423802e-02, -3.28678201e+00, 4.69479355e+00,
-1.04163405e+01, -5.20524024e+00, 7.47774401e-01,
-7.28333260e-01, 1.02762678e+00, -1.25265004e+00,
1.52868387e-01, -6.24779521e-01, 3.34824541e+00,
-3.38433639e-01, -1.25840458e+00],
[ 9.09582169e+01, 1.63531562e+02, 6.76170202e+01,
1.33191732e+01, -2.25146109e+01, -5.07062625e+01,
-2.53086586e+01, 1.52858727e+01, 8.91711589e+00,
-4.85496152e+00, 2.74820618e-01, -2.67000408e+01,
2.70874680e+01, -2.57143726e+01, 9.40861332e+00,
6.22547423e+00, -1.60467598e+00, -2.00925151e+01,
-8.72455807e+01, -7.72219459e+01, 3.12429213e+01,
1.00761797e+00, -2.93258428e+00, -4.31498382e+01,
1.65764127e+00, 5.06411469e-01, 1.19956345e+00,
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0.00000000e+00, 9.00894203e+01, 8.62533437e-01,
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7.69915963e-01, -3.60953781e-01, -3.05457080e+00,
-3.11945796e-01, 2.93483957e+00],
[-2.64304368e+01, -3.75791071e+01, -4.32392637e+01,
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0.00000000e+00, 8.62533437e-01, 3.89261632e+01,
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5.92702363e-01, 1.89214110e-01, 6.00798690e-01,
-8.51544134e-01, 1.70608004e-01, 1.34644497e-01,
8.78530619e-01, -5.63808869e-01],
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4.72942689e+00, 5.60214941e+00, 1.29847795e+01,
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-2.31293472e-03, 1.67533989e-01, -5.63923553e-01,
2.51754003e-01, 3.36401086e-01],
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4.13190786e+00, -2.21753252e+01, -1.19125069e+01,
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2.68076381e+02, -7.59436193e+02, -8.16528029e+02,
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[-3.44918148e+02, 4.15357569e+02, -2.42169445e+03,
2.04760396e+02, -2.40330272e+03, -3.72517496e+02,
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6.06167423e+01, 4.89865614e+02, -1.45333495e+03,
-3.91875375e-01, 3.45192266e+02, -2.86976890e+02,
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1.29935653e+02, -3.04253341e+01, 8.74392556e+00,
1.75290056e+01, 1.99618495e+01, 3.15352228e+00,
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3.26098024e+01, -1.18375096e+02],
[-3.99258173e+03, -7.20567513e+03, -8.37684572e+02,
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9.82568237e+02, -1.85623326e+03, -3.75187556e+03,
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6.20811834e+01, -8.77204845e+00, -2.93896020e+02,
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