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+Update matrices
+===============
+
+
+Consider the following QP
+
+
+.. math::
+  \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}
+
+
+
+We show below how to setup and solve the problem.
+Then we update the matrices :math:`P` and :math:`A` and solve the updated problem
+
+
+.. math::
+  \begin{array}{ll}
+    \mbox{minimize} & \frac{1}{2} x^T \begin{bmatrix}5 & 1.5\\ 1.5 & 1 \end{bmatrix} x + \begin{bmatrix}1 \\ 1\end{bmatrix}^T x \\
+    \mbox{subject to} & \begin{bmatrix}1 \\ 0 \\ 0\end{bmatrix} \leq \begin{bmatrix} 1.2 & 1.1\\ 1.5 & 0\\ 0 & 0.8\end{bmatrix} x \leq \begin{bmatrix}1 \\ 0.7 \\ 0.7\end{bmatrix}
+  \end{array}
+  
+
+
+Python
+------
+
+.. code:: 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
+    # NB: Update only upper triangular part of P
+    P_new = sparse.csc_matrix([[5, 1.5], [1.5, 1]])
+    A_new = sparse.csc_matrix([[1.2, 1.1], [1.5, 0], [0, 0.8]])
+    prob.update(Px=sparse.triu(P_new).data, Ax=A_new.data)
+
+    # Solve updated problem
+    res = prob.solve()
+
+
+
+Matlab
+------
+
+.. code:: 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
+    % NB: Update only upper triangular part of P
+    P_new = sparse([5, 1.5; 1.5, 1]);
+    A_new = sparse([1.2, 1.1; 1.5, 0; 0, 0.8]);
+    prob.update('Px', nonzeros(triu(P_new)), 'Ax', nonzeros(A_new));
+
+    % Solve updated problem
+    res = prob.solve();
+
+
+
+Julia
+------
+
+.. code:: julia
+
+    using OSQP
+    using Compat.SparseArrays, Compat.LinearAlgebra
+
+    # 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
+    # NB: Update only upper triangular part of P
+    P_new = sparse([5. 1.5; 1.5 1.])
+    A_new = sparse([1.2 1.1; 1.5 0.; 0. 0.8])
+    OSQP.update!(prob, Px=triu(P_new).nzval, Ax=A_new.nzval)
+
+    # Solve updated problem
+    results = OSQP.solve!(prob)
+
+
+
+R
+-
+
+.. code:: 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$Solve()
+
+    # Update problem
+    # NB: Update only upper triangular part of P
+    P_new <- Matrix(c(5., 1.5,
+                      1.5, 1.), 2, 2, sparse = TRUE)
+    A_new <- Matrix(c(1.2, 1.5, 0.,
+                      1.1, 0., 0.8), 3, 2, sparse = TRUE)
+    model$Update(Px = P_new@x, Ax = A_new@x)
+
+    # Solve updated problem
+    res <- model$Solve()
+
+
+
+C
+-
+
+.. code:: 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_float P_x_new[3] = {5.0, 1.5, 1.0, };
+        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_float A_x_new[4] = {1.2, 1.5, 1.1, 0.8, };
+        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 = (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
+        if (settings) osqp_set_default_settings(settings);
+
+        // Setup workspace
+        exitflag = osqp_setup(&work, data, settings);
+
+        // Solve problem
+        osqp_solve(work);
+
+        // Update problem
+        // NB: Update only upper triangular part of P
+        osqp_update_P(work, P_x_new, OSQP_NULL, 3);
+        osqp_update_A(work, A_x_new, OSQP_NULL, 4);
+
+        // 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;
+    };