
parameter space in Figure 7.24 because rf(x
1
, x
2
) points in the direction of maximum decrease of
f(x
1
, x
2
), and we are looking at minimizin g the objective function.
Table 7.4 includes the points shown in Figure 7.24, the value of z for the contour, which the
points lie on, the negative gradient vector, and its magnitude. The lengths of the negative gradient
vectors are drawn proportional to their magnitudes given in the table.
A multivariable function like f(x
1
, x
2
) is expandable about a point (x
1
, x
2
) using a two-dimensional
Taylor Series, that is,
f (x
1
, x
2
) ¼ f ( x
1
, x
2
) þ
qf (x
1
, x
2
)
qx
1
(x
1
x
1
) þ
qf (x
1
, x
2
)
qx
2
(x
2
x
2
) þ h:o:t: (7:58)
Objective ...