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J
146 Gradient Optimization
described by
The gradient is
g, = - 400(x,x, - xi) - 2(1- x,),
(5.83)
(5.84)
g,=200(x,-xi).
(5.85)
These equations are programmed in lines 1000-1060 in Program B5-1. There
is a required feature in this BASIC language conversion of the original
FORTRAN program (see lines 1020 and 1030). The objective function must
have the name Q; these two lines then assign this value to either names F or
F9, depending on the value of integer flag Y%. This must be included in each
different objective function subroutine to replace the subroutine argument list
feature found in FORTRAN but missing in BASIC. The shape of this surface,
especially the long, curved valley, is illustrated in Figure 5.23.
x,
3.5
-0.5
x,
-1.0
Figure 5.23. Some level curves for the Rosenbrock function in Equation (5.83). [Reprinted with
permission of Macmillan Publishing Co., Inc. from Introduction to Optimization Techniques by
M. Aoki. Copyright © 1971 by Masanao Aoki.]