Theory and Modern Applications
Table 4 Numerical results of Example 4
From: On q-BFGS algorithm for unconstrained optimization problems
Starting point | BFGS algorithm [23] | ||||
|---|---|---|---|---|---|
it | fe | ge | \(x^{*}\) | \(f(x^{*})\) | |
\((4 , 3)^{T}\) | 31 | 173 | 33 | \((0.999, 0.999)^{T}\) | 7.75e − 16 |
\((-3, 1)^{T}\) | 19 | 115 | 22 | \((0.999, 0.999)^{T}\) | 1.01e − 16 |
\((-1, 3)^{T}\) | 30 | 172 | 35 | \((1.000, 1.000)^{T}\) | 6.33e − 17 |
\((-1.5, 3.7)^{T}\) | 30 | 171 | 35 | \((0.999, 0.999)^{T}\) | 4.14e − 16 |
\((-1 , 4)^{T}\) | 25 | 142 | 29 | \((0.999 , 0.999)^{T}\) | 1.62e − 16 |
\((1, -1)^{T}\) | 15 | 91 | 17 | \((1.000 , 1.000)^{T}\) | 8.33e − 17 |
\((-4, 2)^{T}\) | 27 | 158 | 33 | \((0.999, 0.999)^{T}\) | 1.87e − 15 |
\((-1, -4)^{T}\) | 22 | 132 | 26 | \((1.000 , 1.000)^{T}\) | 3.02e − 16 |
\((-2, 2)^{T}\) | 27 | 149 | 31 | \((0.999 , 0.998)^{T}\) | 8.51e − 15 |
\((-5, 6)^{T}\) | 30 | 171 | 34 | \((0.999 , 0.999)^{T}\) | 4.02e − 16 |
\((-3, 6)^{T}\) | 25 | 149 | 29 | \((0.999, 0.999)^{T}\) | 7.89e − 16 |
\((4, -5)^{T}\) | 22 | 126 | 24 | \((0.999 , 0.999)^{T}\) | 3.90e − 16 |
\((4, -7)^{T}\) | 21 | 128 | 24 | \((1.000 , 1.000)^{T}\) | 1.22e − 15 |
\((-5, -3)^{T}\) | 22 | 125 | 23 | \((0.999 , 0.999)^{T}\) | 1.08e − 15 |
\((4, -5.6)^{T}\) | 24 | 141 | 28 | \((0.999 , 0.999)^{T}\) | 3.96e − 16 |
\((-8, 2)^{T}\) | 11 | 74 | 13 | \((1.000 , 1.000)^{T}\) | 4.03e − 16 |
\((-5, 7)^{T}\) | 30 | 175 | 37 | \((1.000 , 1.000)^{T}\) | 2.70e − 16 |
\((-2, 6)^{T}\) | 36 | 192 | 41 | \((0.999 , 0.999)^{T}\) | 7.46e − 17 |
\((1, -5)^{T}\) | 16 | 97 | 20 | \((1.000 , 1.000)^{T}\) | 2.94e − 16 |
\((-3, -4)^{T}\) | 26 | 151 | 30 | \((0.999 , 0.999)^{T}\) | 1.76e − 16 |
\((8, 1)^{T}\) | 31 | 178 | 34 | \((0.999 , 0.999)^{T}\) | 7.60e − 16 |
\((3, -7)^{T}\) | 12 | 77 | 15 | \((0.999 , 0.999 )^{T}\) | 1.30e − 16 |
\((4, -5)^{T}\) | 22 | 126 | 24 | \((0.999 , 0.999)^{T}\) | 3.90e − 16 |
\((-5, -2)^{T}\) | 21 | 125 | 24 | \((1.000 , 1.000)^{T}\) | 3.63e − 16 |
\((4, -6)^{T}\) | 22 | 134 | 26 | \((0.999 , 0.999)^{T}\) | 7.36e − 16 |
\((3, -4)^{T}\) | 18 | 110 | 23 | \((0.999 , 0.999)^{T}\) | 3.93e − 16 |
\((4, -4)^{T}\) | 24 | 140 | 25 | \((0.999 , 0.999)^{T}\) | 3.97e − 16 |