Example 1. Use the
taxi-cab method to find the minimum of .
Then perform the iterations using the subroutine TaxiCab.
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