QPSolver

QPSolver is a quadratic program solver implemented in C++ using only static memory allocation based on the cvxgen solver. This solver solves optimization problems of the following form

Features

This solver implements the following

• Mehrotra's predictor-corrector
• Permuted LDLT factorization
• KKT system regularization
• Iterative refinement

This solver does not

• Check for feasibility
• Check for boundedness
• Check positive semidefiniteness of the matrix Q

Installation Guide

Download

Download QPSolver with the following command

git clone --recurse-submodules https://github.com/govindchari/QPSolver.git

CMake

To use QPSolver with a CMake project, add the following lines to your CMakeLists.txt file

add_subdirectory(QPSolver)
target_link_libraries(my_library QPSolver)

Example

In this example we will solve a portfolio optimization problem

#include <iostream>
#include "QPSolver.hpp"

int main()
{
    // Setup problem data
    int n = 10;         //Number of assets
    double gamma = 0.5; //Risk aversion parameter
    Eigen::MatrixXd A(1, n);
    Eigen::MatrixXd Q(n, n); //Return Covariance
    Eigen::MatrixXd G(n, n);
    Eigen::VectorXd q(n); //Expected Return
    Eigen::VectorXd b(1);
    Eigen::VectorXd h(n);

    //Generate random return covariance matrix (PSD matrix)
    Q.setRandom();
    Q = Q.transpose() * Q;
    Q += n * Eigen::MatrixXd::Identity(n, n);
    Q *= gamma;

    //Generate random expected return
    q.setRandom();

    //No shorting (non-negativity constraint)
    G = -Eigen::MatrixXd::Identity(n, n);
    h.setZero(n);

    A.setConstant(1);
    b << 1;

    //Set up QPSolver solver
    QP qp(Q, q, A, b, G, h);
    bool verbose = true;

    //Solve QP
    qp.solve(verbose);
    
    //Check solver status
    std::cout << "Converged?" << std::endl;
    std::cout << qp.converged << std::endl;

    //Print optimal portfolio
    std::cout << "x_opt:" << std::endl;
    std::cout << qp.solution.x << std::endl;
}

Examples for equality only, inequality only, and unconstrained probelems can be found in tests