demo.rst

Demo

Consider the following QP

$$\begin{aligned} \begin{array}{ll} \mbox{minimize} & \frac{1}{2} x^T \begin{bmatrix}4 & 1\\ 1 & 2 \end{bmatrix} x + \begin{bmatrix}1 \\ 1\end{bmatrix}^T x \\\ \mbox{subject to} & \begin{bmatrix}1 \\ 0 \\ 0\end{bmatrix} \leq \begin{bmatrix} 1 & 1\\ 1 & 0\\ 0 & 1\end{bmatrix} x \leq \begin{bmatrix}1 \\ 0.7 \\ 0.7\end{bmatrix} \end{array} \end{aligned}$$

We show below how to solve the problem in Python, Matlab, Julia and C.

Python

import osqp
import scipy.sparse as sparse
import numpy as np

# Define problem data
P = sparse.csc_matrix([[4, 1], [1, 2]])
q = np.array([1, 1])
A = sparse.csc_matrix([[1, 1], [1, 0], [0, 1]])
l = np.array([1, 0, 0])
u = np.array([1, 0.7, 0.7])

# Create an OSQP object
prob = osqp.OSQP()

# Setup workspace and change alpha parameter
prob.setup(P, q, A, l, u, alpha=1.0)

# Solve problem
res = prob.solve()

Matlab

% Define problem data
P = sparse([4, 1; 1, 2]);
q = [1; 1];
A = sparse([1, 1; 1, 0; 0, 1]);
l = [1; 0; 0];
u = [1; 0.7; 0.7];

% Create an OSQP object
prob = osqp;

% Setup workspace and change alpha parameter
prob.setup(P, q, A, l, u, 'alpha', 1);

% Solve problem
res = prob.solve();

Julia

import OSQP

# Define problem data
P = sparse([4. 1.; 1. 2.])
q = [1.; 1.]
A = sparse([1. 1.; 1. 0.; 0. 1.])
u = [1.; 0.7; 0.7]
l = [1.; 0.; 0.]

# Crate OSQP object
prob = OSQP.Model()

# Setup workspace and change alpha parameter
OSQP.setup!(prob; P=P, q=q, A=A, l=l, u=u, alpha=1)

# Solve problem
results = OSQP.solve!(prob)

C

#include "osqp.h"

int main(int argc, char **argv) {
    // Load problem data
    c_float P_x[4] = {4.00, 1.00, 1.00, 2.00, };
    c_int P_nnz = 4;
    c_int P_i[4] = {0, 1, 0, 1, };
    c_int P_p[3] = {0, 2, 4, };
    c_float q[2] = {1.00, 1.00, };
    c_float A_x[4] = {1.00, 1.00, 1.00, 1.00, };
    c_int A_nnz = 4;
    c_int A_i[4] = {0, 1, 0, 2, };
    c_int A_p[3] = {0, 2, 4, };
    c_float l[3] = {1.00, 0.00, 0.00, };
    c_float u[3] = {1.00, 0.70, 0.70, };
    c_int n = 2;
    c_int m = 3;

    // Problem settings
    OSQPSettings * settings = (OSQPSettings *)c_malloc(sizeof(OSQPSettings));

    // Structures
    OSQPWorkspace * work;  // Workspace
    OSQPData * data;  // OSQPData

    // Populate data
    data = (OSQPData *)c_malloc(sizeof(OSQPData));
    data->n = n;
    data->m = m;
    data->P = csc_matrix(data->n, data->n, P_nnz, P_x, P_i, P_p);
    data->q = q;
    data->A = csc_matrix(data->m, data->n, A_nnz, A_x, A_i, A_p);
    data->l = l;
    data->u = u;


    // Define Solver settings as default
    osqp_set_default_settings(settings);
    settings->alpha = 1.0; // Change alpha parameter

    // Setup workspace
    work = osqp_setup(data, settings);

    // Solve Problem
    osqp_solve(work);

    // Cleanup
    osqp_cleanup(work);
    c_free(data->A);
    c_free(data->P);
    c_free(data);
    c_free(settings);

    return 0;
};