saddle-ghc.hs

import Common

saddle = let start = [1, 1]
             f x1 y1 x2 y2 = ((sqr x1) + (sqr y1)) - ((sqr x2) + (sqr y2))
             [x1_star, y1_star] =
                 multivariate_argmin
                 (\ [x1, y1] ->
                      multivariate_max
                      (\ [x2, y2] -> f (lift x1) (lift y1) x2 y2)
                      (map lift start))
                 start
             [x2_star, y2_star] =
                 multivariate_argmax
                 (\ [x2, y2] -> f (lift x1_star) (lift y1_star) x2 y2)
                 start
         in [[x1_star, y1_star], [x2_star, y2_star]]

main = print saddle