# 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 <stdlib.h>
#include "osqp.h"

int main(int argc, char **argv) {
OSQPFloat P_x[3] = {4.0, 1.0, 2.0, };
OSQPInt P_nnz = 3;
OSQPInt P_i[3] = {0, 0, 1, };
OSQPInt P_p[3] = {0, 1, 3, };
OSQPFloat q[2] = {1.0, 1.0, };
OSQPFloat A_x[4] = {1.0, 1.0, 1.0, 1.0, };
OSQPInt A_nnz = 4;
OSQPInt A_i[4] = {0, 1, 0, 2, };
OSQPInt A_p[3] = {0, 2, 4, };
OSQPFloat l[3] = {1.0, 0.0, 0.0, };
OSQPFloat u[3] = {1.0, 0.7, 0.7, };
OSQPInt n = 2;
OSQPInt m = 3;

/* Exitflag */
OSQPInt exitflag = 0;

/* Solver, settings, matrices */
OSQPSolver   *solver;
OSQPSettings *settings;
OSQPCscMatrix* P = malloc(sizeof(OSQPCscMatrix));
OSQPCscMatrix* A = malloc(sizeof(OSQPCscMatrix));

/* Populate matrices */
csc_set_data(A, m, n, A_nnz, A_x, A_i, A_p);
csc_set_data(P, n, n, P_nnz, P_x, P_i, P_p);

/* Set default settings */
settings = (OSQPSettings *)malloc(sizeof(OSQPSettings));
if (settings) {
osqp_set_default_settings(settings);
settings->alpha = 1.0; /* Change alpha parameter */
}

/* Setup solver */
exitflag = osqp_setup(&solver, P, q, A, l, u, m, n, settings);

/* Solve problem */
if (!exitflag) exitflag = osqp_solve(solver);

/* Cleanup */
osqp_cleanup(solver);
if (A) free(A);
if (P) free(P);
if (settings) free(settings);

return (int)exitflag;
};