Epigraph is a modern C++ interface to formulate and solve linear, quadratic and second order cone problems. It makes use of Eigen types and operator overloading for straightforward problem formulation.
- Flexible and intuitive way to formulate LPs, QPs and SOCPs
- Dynamic parameters that can be changed without re-formulating the problem
- Automatically clean up the problem and remove unused variables
- Print the problem formulation and solver data for inspection
The solvers are included as submodules for convenience. Note that some solvers have more restrictive licenses which automatically override the Epigraph license when activated. Pass the listed argument to cmake during configuration to enable the solvers.
- OSQP
-DENABLE_OSQP=TRUE
. Apache-2.0 License.
git clone --recurse-submodules https://github.com/EmbersArc/Epigraph
To use Epigraph with a cmake project, simply enable the desired solvers, include the subdirectory and link the library.
set(ENABLE_OSQP TRUE)
set(ENABLE_ECOS TRUE)
set(ENABLE_EICOS TRUE)
add_subdirectory(Epigraph)
target_link_libraries(my_library epigraph)
#include "epigraph.hpp"
#include <fmt/format.h>
#include <fmt/ostream.h>
// This example solves the portfolio optimization problem in QP form
using namespace cvx;
int main()
{
size_t n = 5; // Assets
size_t m = 2; // Factors
fmt::print("Running with assets: {}, factors: {}\n", n, m);
// Set up problem data.
double gamma = 0.5; // risk aversion parameter
Eigen::VectorXd mu(n); // vector of expected returns
Eigen::MatrixXd F(n, m); // factor-loading matrix
Eigen::VectorXd D(n); // diagonal of idiosyncratic risk
Eigen::MatrixXd Sigma(n, n); // asset return covariance
mu.setRandom();
F.setRandom();
D.setRandom();
mu = mu.cwiseAbs();
F = F.cwiseAbs();
D = D.cwiseAbs();
Sigma = F * F.transpose();
Sigma.diagonal() += D;
// Formulate QP.
OptimizationProblem qp;
// Declare variables with...
// addVariable(name) for scalars,
// addVariable(name, rows) for vectors and
// addVariable(name, rows, cols) for matrices.
VectorX x = op.addVariable("x", n);
// Available constraint types are equalTo(), lessThan(), greaterThan() and box()
qp.addConstraint(greaterThan(x, 0.));
qp.addConstraint(equalTo(x.sum(), 1.));
// Make mu dynamic in the cost function so we can change it later
qp.addCostTerm(x.transpose() * par(gamma * Sigma) * x - dynpar(mu).dot(x));
// Print the problem formulation for inspection
fmt::print("{}\n", qp);
// Create and initialize the solver instance.
osqp::OSQPSolver solver(qp);
// Print the canonical problem formulation for inspection
fmt::print("{}\n", solver);
// Solve problem and show solver output
solver.solve(true);
fmt::print("Solver result: {} ({})\n", solver.getResultString(), solver.getExitCode());
// Call eval() to get the variable values
fmt::print("Solution 1:\n {}\n", eval(x));
// Update data
mu.setRandom();
mu = mu.cwiseAbs();
// Solve again
// OSQP will warm start automatically
solver.solve(true);
fmt::print("Solver result: {} ({})\n", solver.getResultString(), solver.getExitCode());
fmt::print("Solution 2:\n {}\n", eval(x));
}
See the tests for more examples, including the same problem in SOCP form.
The following terms may be passed to the contraint functions:
Function | Allowed expressions |
---|---|
equalTo() |
Affine == Affine |
lessThan() |
Affine <= Affine or Norm2 + Affine <= Affine (SOCP) |
greaterThan() |
Affine >= Affine or Affine >= Norm2 + Affine (SOCP) |
box() |
Affine <= Affine <= Affine |
addCostTerm() |
Affine (SOCP) or QuadForm + Affine (QP) |
With the following expressions:
Expression | Form |
---|---|
Affine |
p1 * x1 + p2 * x2 + ... + c |
Norm2 |
(Affine1^2 + Affine2^2 + ...)^(1/2) |
QuadForm |
x' * P * x where P is Hermitian |