Quadratic Constrained Quadratic Programming problem

scs-eigen can be used to solve Quadratic Constrained Quadratic Programming (QCQP) problems in the for

where is the optimization variable. The objective function is defined by a positive semidefinite matrix and vector . The quadratic constraints are defined positive semidefinite matrices and vectors .

The following example shows how scs-eigen can be used to solve the QCQP problem:

First of all you should include ScsEigen

#include <ScsEigen/ScsEigen.h>

You can also define the Hessian, gradient the constraint matrix and vectors.

Eigen::Matrix2d H;
H << 3, 2,
     2, 4;
Eigen::Vector2d gradient;
gradient << 3, 1;

Eigen::Matrix2d A = 2 * Eigen::Matrix2d::Identity();
Eigen::Vector2d b;
b << -4, -5;

double upperBound = -1;

Once the matrices used to described the QCQP problem have been defined you can create ScsEigen::Solver and initialize the number of variables.

ScsEigen::Solver solver;
solver.setNumberOfVariabels(2);

Now you can set the constraints and the cost using ScsEigen::MathematicalProgram class

solver.mathematicalProgram().addQuadraticConstraint(
        std::make_shared<ScsEigen::QuadraticConstraint>(A, b, upperBound),
        "quadratic constraint");

solver.mathematicalProgram().addQuadraticCost(
        std::make_shared<ScsEigen::QuadraticCost>(H, gradient),
        "quadratic cost");

You can finally solve the problem and get the solution

solver.solve();
Eigen::Vector2d solution = solver.solution().solution;

The complete example follows

### CMakeLists.txt
project(QCQP)
find_package(ScsEigen REQUIRED)
add_executable(QCQP qcqp.cpp)
target_link_libraries(QCQP ScsEigen::ScsEigen)

/// qp.cpp

#include <ScsEigen/ScsEigen.h>

#include <Eigen/Dense>

int main()
{
    Eigen::Matrix2d H;
    H << 3, 2,
         2, 4;

    Eigen::Vector2d gradient;
    gradient << 3, 1;

    Eigen::Matrix2d A = 2 * Eigen::Matrix2d::Identity();
    Eigen::Vector2d b;
    b << -4, -5;

    ScsEigen::Solver solver;

    solver.mathematicalProgram().setNumberOVfariables(2);

    if (!solver.mathematicalProgram().addQuadraticCost(
        std::make_shared<ScsEigen::QuadraticCost>(H, gradient),
        "quadratic cost"))
        return EXIT_FAILURE;


    if (!solver.mathematicalProgram().addQuadraticConstraint( //
        std::make_shared<ScsEigen::QuadraticConstraint>(A, b, upperBound),
        "quadratic constraint"))
        return EXIT_FAILURE;

    if (!solver.solve())
        return EXIT_FAILURE;
    if (!solver.solution().isValid())
        return EXIT_FAILURE;
    if (solver.solution().status != ScsEigen::Solution::Status::solved)
        return EXIT_FAILURE;

    Eigen::Vector2d solution = solver.solution().solution;

    return EXIT_SUCCESS;
}