Question 10.12: Apply the method of Hook and Jeeves to the objective functio......
Apply the method of Hook and Jeeves to the objective function defined in Example 10.9,\ f(C) = 3C^2_1 + 2C_1C_2 + 3C^2_2 – 16C_1 – 8C_2 .
Since Hook and Jeeves has three directions, there are now three direction vector indicators: η = 1, η = 2, and η = 3. These, along with the consequences of each direction vector, need to be incorporated in both the main program cyclic and golden. The function objective reduces to a single line since the explicit formula for f(C) is given.
The resulting sequence of points is given in Table 10.7 and graphed in Figure 10.25. As should be expected, the method of Hook and Jeeves gives results better than those of cyclic coordinates since the optimal point is approached from a variety of directions.
TABLE 10.7 Sequence of Iterations for Example 10.12 Using the
Hook and Jeeves Algorithm
\ \begin{array}{c} \hline i&C^{(i)}&v^{(i)}&\xi&f(C^{(i)})\\\hline 0&(0.00,0.00)&(1,0)&1.05&0.000\\1&(2.67,0.00)&(0,1)&0.44&-21.333\\2&(2.67,0.44)&(1,1)&-0.15&-21.923\\ 3& (2.62,0.39)&(1,0)&0.05&-21.990\\4&(2.54,0.39)&(0,1)&-0.02&-22.000\\5&(2.54,0.49)&(1,1)&0.01&-22.000\\ 6& (2.53,0.48)&(1,0)&0.00&-22.000\\7&(2.51,0.48)&(0,1)&0.00&-22.000\\8&(2.51,0.50)&(1,1)&0.00&-22.000\\9&(2.51,0.50)&(1,0)&0.00&-22.000\\10&(2.50,0.50)&(0,1)&0.00&-22.000\\\hline \end{array}
