Function

Initial Point

Optimal Solution

Number of Iterations

Expected

Calculated

Case 1

Case 3

Case 4

Basic Function (Steepest Ascent)

$\left\{\begin{array}{c}1\\ 1\\ 1\end{array}\right\}$

$\left\{\begin{array}{c}1.570\\ 0\\ -1.570\end{array}\right\}$

$\left\{\begin{array}{c}1.570\\ 0\\ -1.571\end{array}\right\}$

3084

68

1546

Himmelblau’s Function (Steepest Descent)

$\left\{\begin{array}{c}1\\ 1\end{array}\right\}$

$\left\{\begin{array}{c}3\\ 2\end{array}\right\}$

$\left\{\begin{array}{c}2.999\\ 2.000\end{array}\right\}$

2305

91

1156

$\left\{\begin{array}{c}-1\\ 1\end{array}\right\}$

$\left\{\begin{array}{c}-2.805\\ 3.131\end{array}\right\}$

$\left\{\begin{array}{c}-2.805\\ 3.131\end{array}\right\}$

2.882

73

1442

$\left\{\begin{array}{c}1\\ -1\end{array}\right\}$

$\left\{\begin{array}{c}3.584\\ -1.848\end{array}\right\}$

$\left\{\begin{array}{c}3.584\\ -1.848\end{array}\right\}$

3165

90

1588

$\left\{\begin{array}{c}-1\\ -1\end{array}\right\}$

$\left\{\begin{array}{c}-3.779\\ -3.283\end{array}\right\}$

$\left\{\begin{array}{c}-3.780\\ -3.283\end{array}\right\}$

3793

87

1899

Trid Function (Steepest Descent)

$\left\{\begin{array}{c}1\\ 1\\ 1\\ 1\\ 1\\ 1\end{array}\right\}$

$\left\{\begin{array}{c}6\\ 10\\ 12\\ 12\\ 10\\ 6\end{array}\right\}$

$\left\{\begin{array}{c}5.999\\ 9.999\\ 11.999\\ 11.999\\ 9.999\\ 5.999\end{array}\right\}$

21,303

85

10,623