
451-D Optimization Algorithms
where
µ =
+ −
− +
′
′ ′
f x w z
f x f x w
( )
( ) ( )
2
2 1
2
(2.10)
z
f x f x
x x
f x f x=
−
−
+ +
′ ′
3
1 2
2 1
1 2
( ) ( )
( ) ( ) (2.11)
w
x x
x x
z f x f x=
−
−
+ −
′ ′
2 1
2 1
2
1 2
( ) ( )
(2.12)
The algorithm for this method is coded in MATLAB (cubic.m) and is described
in Table 2.4.
On executing the code for the test problem, the output obtained is
a b
-------------------------
40.000 65.000
54.109 65.000
54.109 55.120
-------------------------
x* = 55.084 Minimum = 1225.166
Number of function calls = 28
This method is able to capture the minimum point of the function with the
number of function evaluations comparable to that in the ...