Question

8.26. This problem considers the various steps used in the Nelder-Mead method (a) For the top contour plot in Figure 8.33, explain which step from Table 8.5 was used to determine each triangle. (b) For the bottom contour plot in Figure 8.33, explain which step from Table 8.5 was used to determine each triangle. Pick a > 0 (e.g., a = 1) and B with 0

Answer 1

For the top contour plot in Fig. 8.33, first use Step 0 and Step 1 to construct triangles 3 and 4. Then apply Step 3 (Reflection) to construct triangle 2. Note that triangles 2 and 3 are reflections of each other. Similarly triangles 1 and 4 are also reflections of each other. So construct triangle 1 with the help of Step 3 (Reflection) using triangle 4.

For the bottom contour plot in Fig. 8.33, first use Step 0 and Step 1 to construct triangles 3, 4 and 5. Next, Step 3 (Reflection) was used to construct triangles 2 and 1. Note that triangles 2 and 3 are reflections of each other. Similarly triangles 1 and 4 are also reflections of each other. However for triangle 5, use Step 0 and Step 1.