Squashed 'third_party/osqp/' content from commit 33454b3e23
Change-Id: I056df0582ca06664e86554c341a94c47ab932001
git-subtree-dir: third_party/osqp
git-subtree-split: 33454b3e236f1f44193bfbbb6b8c8e71f8f04e9a
Signed-off-by: Austin Schuh <austin.linux@gmail.com>
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+Setup and solve
+===============
+
+
+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 solve the problem in Python, Matlab, Julia and C.
+
+
+
+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 and change alpha parameter
+ prob.setup(P, q, A, l, u, alpha=1.0)
+
+ # Solve 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 and change alpha parameter
+ prob.setup(P, q, A, l, u, 'alpha', 1);
+
+ % Solve problem
+ res = prob.solve();
+
+
+
+Julia
+------
+
+.. code:: 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
+-
+
+.. 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)
+
+ # 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
+-
+
+.. 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_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
+ 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;
+ };