Example 2.  Use the taxi-cab method to find the minimum of   [Graphics:Images/PowellMethodMod_gr_30.gif].  

Solution 2.

Enter the function [Graphics:../Images/PowellMethodMod_gr_31.gif].



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.  
3D plot of the points  [Graphics:../Images/PowellMethodMod_gr_36.gif]  involved in the iteration is given below.  


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


























(c) John H. Mathews 2004