are shown in fig8 a reduction every vertex is reduced in the direction of x 1 in the case of the two dimensions it is shown in fig8 b fig9 illustrates an algorithm for searching for an optimum point by the simplex method next the maximum point the worst point x h the second maximum point x s and the minimum point x 1 are defined step 12 when these values are converged step 13 the procedure is terminated if the procedure is not terminated the reflection positions x r and f x r of the worst point x h with respect to x are obtained step 14 and are compared with f x r and f x s step 15 in this case if f x r u2266 f x s and f x r u2267 f x 1 step 16 the worst point x h is eliminated and x h is replaced by x r step 17 if f x r lt f x 1 in the step 16 x e and f x e are obtained step 18 and if f x e lt f x 1 step 19 x h is replaced by x e step.