#include <vector>
#include <functional>

using namespace std;
using Vec = vector<double>;

Vec operator+(const Vec& a, const Vec& b);
Vec operator-(const Vec& a, const Vec& b);
Vec operator*(double s, const Vec& a);
double norm(const Vec& a);

double line_search(
    const Vec& x,
    const Vec& dir,
    function<double(Vec)> obj,
    double a = -1.,
    double b = 1.
);

Vec powell(
    Vec x,
    function<double(Vec)> obj,
    double tol = 1e-8,
    int max_iter = 200
);