osqp-cpp: A C++ wrapper for OSQP

A C++ wrapper for OSQP, an ADMM-based solver for quadratic programming.

Compared with OSQP's native C interface, the wrapper provides a more convenient input format using Eigen sparse matrices and handles the lifetime of the OSQPWorkspace struct. This package has similar functionality to osqp-eigen.

The full API is documented in-line in osqp++.h. We describe only the input format in this README.

Note: OSQP uses looser default tolerances than other similar solvers. We recommend looking at the description of the convergence tolerances in Section 3.4 of the OSQP paper and adjusting tolerances via the OsqpSettings struct as appropriate.

This is not an officially supported Google product.

OsqpInstance format

OSQP solves the convex quadratic optimization problem:

min_x 0.5 * x'Px + q'x
s.t.  l <= Ax <= u

where P is a symmetric positive semi-definite matrix.

The inequalities are component-wise, and equalities may be enforced by setting l[i] == u[i] for some row i. Single-sided inequalities can be enforced by setting the lower or upper bounds to negative or positive infinity (std::numeric_limits<double>::infinity()), respectively.

This maps to the OsqpInstance struct in osqp++.h as follows.

• objective_matrix is P.
• objective_vector is q.
• constraint_matrix is A.
• lower_bounds is l.
• upper_bounds is u.

Example usage

The code below formulates and solves the following 2-dimensional optimization problem:

min_(x,y) x^2 + 0.5 * x * y + y^2 + x
s.t.      x >= 1

const double kInfinity = std::numeric_limits<double>::infinity();
SparseMatrix<double> objective_matrix(2, 2);
const Triplet<double> kTripletsP[] = {
    {0, 0, 2.0}, {1, 0, 0.5}, {0, 1, 0.5}, {1, 1, 2.0}};
objective_matrix.setFromTriplets(std::begin(kTripletsP),
                                   std::end(kTripletsP));

SparseMatrix<double> constraint_matrix(1, 2);
const Triplet<double> kTripletsA[] = {{0, 0, 1.0}};
constraint_matrix.setFromTriplets(std::begin(kTripletsA),
                                      std::end(kTripletsA));

OsqpInstance instance;
instance.objective_matrix = objective_matrix;
instance.objective_vector.resize(2);
instance.objective_vector << 1.0, 0.0;
instance.constraint_matrix = constraint_matrix;
instance.lower_bounds.resize(1);
instance.lower_bounds << 1.0;
instance.upper_bounds.resize(1);
instance.upper_bounds << kInfinity;

OsqpSolver solver;
OsqpSettings settings;
// Edit settings if appropriate.
auto status = solver.Init(instance, settings);
// Assuming status.ok().
OsqpExitCode exit_code = solver.Solve();
// Assuming exit_code == OsqpExitCode::kOptimal.
double optimal_objective = solver.objective_value();
Eigen::VectorXd optimal_solution = solver.primal_solution();

Installation

osqp-cpp requires CMake, a C++17 compiler, and the following packages:

• OSQP
• abseil-cpp
• Eigen
• googletest (for testing only)

On Debian/Ubuntu systems you may install Eigen via the libeigen3-dev package.

osqp-cpp will attempt to automatically detect if the necessary targets exist as part of the same project. If the necessary OSQP, abseil-cpp, or googletest targets are not found, osqp-cpp will attempt to download the sources from their GitHub repositories through the use of CMake's FetchContent functionality. If the Eigen3 targets are not found, osqp-cpp will attempt to find Eigen3 as a system package. To prevent osqp-cpp from unnecessarily downloading target dependencies, please ensure that any target dependencies that are already available are included before osqp-cpp.

To build osqp-cpp, run the following from the osqp-cpp directory:

$ mkdir build; cd build
$ cmake ..
$ make
$ make test

So far, the interface has been tested only on Linux. Contributions to support additional platforms are welcome.

FAQ

• Is OSQP deterministic?
  • No, not in its default configuration. Section 5.2 of the OSQP paper describes that the update rule for the step size rho depends on the ratio between the runtime of the iterations and the runtime of the numerical factorization. Setting adaptive_rho to false disables this update rule and makes OSQP deterministic, but this could significantly slow down OSQP's convergence.