In this problem you will do some further experiments with contour. Recall the steepest descent algorithm you programmed in Assignment 3. There, we had used the steepest descent algorithm to solve the following optimization problem (iteratively): minXER2 f(x) = 1/2 xT Ax - xTb
Now we want to plot the path taken by the iterates of the algorithm over the contour plot of f(x). The function showPath. m which you can download from course webpage does this; this function has the following header:
showPath(A, B,XVals)
Here A and b characterize (1), and the matrix XVals contains the iterates of the steepest descent algorithm as its rows; that is XVals looks like the following
XVals =
-3.0000 -2.0000
-1.3589 -0.1245
-0.3634 -0.9956
0.0414 -0.5329
0.2870 -0.7478
First, you need to revise your steepest descent routine so that the iterates of the algorithm are stored as rows of the matrix XVals. Then, revise the function header to have XVals as another output:
function [x F it XVals] = steep(x0, A, b, itmax)
Then, you can use showPath to plot the path taken by the iterates. Run your tests on the following problem.
A = [2 0 2 6], b = [1 4], x0 = [-3 -2]
Your result at this point should like Figure 1.
Once you have everything working, revise showPath by having more contour lines and having the contour lines labeled (using clabel). Submit the revised steep and showPath functions and your final plot.