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/*
* This example shows how to formulate and solve the following QP problem:
* https://osqp.org/docs/examples/setup-and-solve.html
*
* Minimize
* Objective:
* 1/2(4x1^2 + 2x1x2 + 2x2^2) + (x1 + x2) + 0 or in the matrix form
* 1/2 x^T|4 1|x + |1|^Tx + 0
* |1 2| |1|
* Subject to
* 1 <= x1 + x2 <= 1
* 0 <= x1 <= 0.7
* 0 <= x2 <= 0.7 or in the matrix form
* |1| |1 1| |1.0|
* |0| <= |1 0|x <= |0.7|
* |0| |0 1| |0.7|
*
* Expected results: x1 = 0.3; x2 = 0.7;
*/
#include <vector>
#include <iostream>
#include <CGAL/Simple_cartesian.h>
#include <CGAL/OSQP_quadratic_program_traits.h>
using Kernel = CGAL::Simple_cartesian<double>;
using FT = typename Kernel::FT;
int main(void) {
const std::size_t n = 2; // number of variables
const std::size_t m = 3; // number of constraints
CGAL::OSQP_quadratic_program_traits<FT> osqp(n, m);
osqp.set_P(0, 0, 4);
osqp.set_P(0, 1, 1);
osqp.set_P(1, 1, 2);
osqp.set_q(0, 1);
osqp.set_q(1, 1);
osqp.set_r(0);
osqp.set_A(0, 0, 1);
osqp.set_A(0, 1, 1);
osqp.set_A(1, 0, 1);
osqp.set_A(2, 1, 1);
osqp.set_l(0, 1);
osqp.set_l(1, 0);
osqp.set_l(2, 0);
osqp.set_u(0, 1);
osqp.set_u(1, 0.7);
osqp.set_u(2, 0.7);
std::vector<FT> x; x.reserve(2);
osqp.solve(std::back_inserter(x));
std::cout << "solution (x1 x2): ";
for (const FT value : x) {
std::cout << value << "; ";
}
std::cout << std::endl;
}
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