# Update vectors¶

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 setup and solve the problem. Then we update the vectors $$q$$, $$l$$, and $$u$$ and solve the updated problem

$\begin{split}\begin{array}{ll} \mbox{minimize} & \frac{1}{2} x^T \begin{bmatrix}4 & 1\\ 1 & 2 \end{bmatrix} x + \begin{bmatrix}2 \\ 3\end{bmatrix}^T x \\ \mbox{subject to} & \begin{bmatrix}2 \\ -1 \\ -1\end{bmatrix} \leq \begin{bmatrix} 1 & 1\\ 1 & 0\\ 0 & 1\end{bmatrix} x \leq \begin{bmatrix}2 \\ 2.5 \\ 2.5\end{bmatrix} \end{array}\end{split}$

## 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
prob.setup(P, q, A, l, u)

# Solve problem
res = prob.solve()

# Update problem
q_new = np.array([2, 3])
l_new = np.array([2, -1, -1])
u_new = np.array([2, 2.5, 2.5])
prob.update(q=q_new, l=l_new, u=u_new)

# Solve updated 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
prob.setup(P, q, A, l, u);

% Solve problem
res = prob.solve();

% Update problem
q_new = [2; 3];
l_new = [2; -1; -1];
u_new = [2; 2.5; 2.5];
prob.update('q', q_new, 'l', l_new, 'u', u_new);

% Solve updated 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
OSQP.setup!(prob; P=P, q=q, A=A, l=l, u=u)

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

# Update problem
q_new = [2.; 3.]
l_new = [2.; -1.; -1.]
u_new = [2.; 2.5; 2.5]
OSQP.update!(prob, q=q_new, l=l_new, u=u_new)

# Solve updated 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)

# Setup workspace
model <- osqp(P, q, A, l, u)

# Solve problem
res <- model$Solve() # Update problem q_new <- c(2., 3.) l_new <- c(2., -1., -1.) u_new <- c(2., 2.5, 2.5) model$Update(q = q_new, l = l_new, u = u_new)

# Solve updated problem
res <- model\$Solve()


## C¶

#include "osqp.h"

int main(int argc, char **argv) {
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 q_new[2] = {2.0, 3.0, };
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 l_new[3] = {2.0, -1.0, -1.0, };
c_float u[3] = {1.0, 0.7, 0.7, };
c_float u_new[3] = {2.0, 2.5, 2.5, };
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);

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

// Solve problem
osqp_solve(work);

// Update problem
osqp_update_lin_cost(work, q_new);
osqp_update_bounds(work, l_new, u_new);

// Solve updated problem
osqp_solve(work);

// Cleanup
osqp_cleanup(work);
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;
};