Function find_min_single_variable

dlib/optimization/optimization_line_search.h:573–850

    template <typename funct>
    double find_min_single_variable (
        const funct& f,
        double& starting_point,
        const double begin = -1e200,
        const double end = 1e200,
        const double eps = 1e-3,
        const long max_iter = 100,
        const double initial_search_radius = 1
    )
    {
        DLIB_CASSERT( eps > 0 &&
                      max_iter > 1 &&
                      begin <= starting_point && starting_point <= end && 
                      initial_search_radius > 0,
                      "eps: " << eps
                      << "\n max_iter: "<< max_iter 
                      << "\n begin: "<< begin 
                      << "\n end:   "<< end 
                      << "\n starting_point: "<< starting_point 
                      << "\n initial_search_radius: "<< initial_search_radius 
        );

        double search_radius = initial_search_radius;

        double p1=0, p2=0, p3=0, f1=0, f2=0, f3=0;
        long f_evals = 1;

        if (begin == end)
        {
            return f(starting_point);
        }

        using std::abs;
        using std::min;
        using std::max;

        // find three bracketing points such that f1 > f2 < f3.   Do this by generating a sequence
        // of points expanding away from 0.   Also note that, in the following code, it is always the
        // case that p1 < p2 < p3.



        // The first thing we do is get a starting set of 3 points that are inside the [begin,end] bounds
        p1 = max(starting_point-search_radius, begin);
        p3 = min(starting_point+search_radius, end);
        f1 = f(p1);
        f3 = f(p3);

        if (starting_point == p1 || starting_point == p3)
        {
            p2 = (p1+p3)/2;
            f2 = f(p2);
        }
        else
        {
            p2 = starting_point;
            f2 = f(starting_point);
        }