Example 3.  Use Powell's method to find the minimum of   .  

Solution 3.

Then perform the iterations using the subroutine Powell.

Observe that in each iteration of the taxi-cab method only one variable in the point is changing.  Convergence proceeds a polygonal path where the segments are parallel to the coordinate axes.  If the geometry of level curves is sufficiently complicated it might not be feasible to zig-zag to the minimum in this manner.

Let us compare this answer with Mathematica's built in procedure FindMinimum.

(c) John H. Mathews 2004