Setup and solve

Consider the following QP

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

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

Python

import osqp
import numpy as np
from scipy import sparse

# 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

using OSQP
using Compat.SparseArrays

# 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]

# 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)

R

library(osqp)
library(Matrix)

# Define problem data
P <- Matrix(c(4., 1.,
              1., 2.), 2, 2, sparse = TRUE)
q <- c(1., 1.)
A <- Matrix(c(1., 1., 0.,
              1., 0., 1.), 3, 2, sparse = TRUE)
l <- c(1., 0., 0.)
u <- c(1., 0.7, 0.7)

# Change alpha parameter and setup workspace
settings <- osqpSettings(alpha = 1.0)
model <- osqp(P, q, A, l, u, settings)

# Solve problem
res <- model$Solve()

C

#include "osqp.h"

int main(int argc, char **argv) {
    // Load problem data
    c_float P_x[3] = {4.0, 1.0, 2.0, };
    c_int P_nnz = 3;
    c_int P_i[3] = {0, 0, 1, };
    c_int P_p[3] = {0, 1, 3, };
    c_float q[2] = {1.0, 1.0, };
    c_float A_x[4] = {1.0, 1.0, 1.0, 1.0, };
    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] = {1.0, 0.0, 0.0, };
    c_float u[3] = {1.0, 0.7, 0.7, };
    c_int n = 2;
    c_int m = 3;

    // Exitflag
    c_int exitflag = 0;

    // Workspace structures
    OSQPWorkspace *work;
    OSQPSettings  *settings = (OSQPSettings *)c_malloc(sizeof(OSQPSettings));
    OSQPData      *data     = (OSQPData *)c_malloc(sizeof(OSQPData));

    // Populate data
    if (data) {
        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
    if (settings) {
        osqp_set_default_settings(settings);
        settings->alpha = 1.0; // Change alpha parameter
    }

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

    // Solve Problem
    osqp_solve(work);

    // Cleanup
    if (data) {
        if (data->A) c_free(data->A);
        if (data->P) c_free(data->P);
        c_free(data);
    }
    if (settings) c_free(settings);

    return exitflag;
};