**Example 1.** Use the
taxi-cab method to find the minimum of .

**Solution 1.**

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