Function main

examples/optimization_ex.cpp:116–319

// ----------------------------------------------------------------------------------------

int main() try
{
    // Set the starting point to (4,8).  This is the point the optimization algorithm
    // will start out from and it will move it closer and closer to the function's 
    // minimum point.   So generally you want to try and compute a good guess that is
    // somewhat near the actual optimum value.
    column_vector starting_point = {4, 8};

    // The first example below finds the minimum of the rosen() function and uses the
    // analytical derivative computed by rosen_derivative().  Since it is very easy to
    // make a mistake while coding a function like rosen_derivative() it is a good idea
    // to compare your derivative function against a numerical approximation and see if
    // the results are similar.  If they are very different then you probably made a 
    // mistake.  So the first thing we do is compare the results at a test point: 
    cout << "Difference between analytic derivative and numerical approximation of derivative: " 
         << length(derivative(rosen)(starting_point) - rosen_derivative(starting_point)) << endl;


    cout << "Find the minimum of the rosen function()" << endl;
    // Now we use the find_min() function to find the minimum point.  The first argument
    // to this routine is the search strategy we want to use.  The second argument is the 
    // stopping strategy.  Below I'm using the objective_delta_stop_strategy which just 
    // says that the search should stop when the change in the function being optimized 
    // is small enough.

    // The other arguments to find_min() are the function to be minimized, its derivative, 
    // then the starting point, and the last is an acceptable minimum value of the rosen() 
    // function.  That is, if the algorithm finds any inputs to rosen() that gives an output 
    // value <= -1 then it will stop immediately.  Usually you supply a number smaller than 
    // the actual global minimum.  So since the smallest output of the rosen function is 0 
    // we just put -1 here which effectively causes this last argument to be disregarded.

    find_min(bfgs_search_strategy(),  // Use BFGS search algorithm
             objective_delta_stop_strategy(1e-7), // Stop when the change in rosen() is less than 1e-7
             rosen, rosen_derivative, starting_point, -1);
    // Once the function ends the starting_point vector will contain the optimum point 
    // of (1,1).
    cout << "rosen solution:\n" << starting_point << endl;


    // Now let's try doing it again with a different starting point and the version
    // of find_min() that doesn't require you to supply a derivative function.  
    // This version will compute a numerical approximation of the derivative since 
    // we didn't supply one to it.
    starting_point = {-94, 5.2};
    find_min_using_approximate_derivatives(bfgs_search_strategy(),
                                           objective_delta_stop_strategy(1e-7),
                                           rosen, starting_point, -1);
    // Again the correct minimum point is found and stored in starting_point
    cout << "rosen solution:\n" << starting_point << endl;


    // Here we repeat the same thing as above but this time using the L-BFGS 
    // algorithm.  L-BFGS is very similar to the BFGS algorithm, however, BFGS 
    // uses O(N^2) memory where N is the size of the starting_point vector.  
    // The L-BFGS algorithm however uses only O(N) memory.  So if you have a 
    // function of a huge number of variables the L-BFGS algorithm is probably 
    // a better choice.