Table 2 Influence of the step size parameters \(\beta_{n}\) and \(\lambda_{n}\) (cases 4–6) of algorithm (3.1) for different initial points
Case → | Case 4 | Case 5 | Case 6 | ||||||
|---|---|---|---|---|---|---|---|---|---|
#Initial point ↓ | Iters | Time (s) | Sol | Iters | Time (s) | Sol | Iters | Time (s) | Sol |
\((0,0)^{\top }\) | 1647 | 0.650587 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.249753\cr0\end{matrix}} \Bigr )\) | 106 | 0.176374 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.249991\cr0\end{matrix}} \Bigr )\) | 56 | 0.124235 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.249996\cr0\end{matrix}} \Bigr )\) |
\((1,1)^{\top }\) | 790 | 0.398679 | \(\Bigl ({\scriptsize\begin{matrix}{} 1.124877\cr0.875123\end{matrix}} \Bigr )\) | 51 | 0.122999 | \(\Bigl ({\scriptsize\begin{matrix}{} 1.124996\cr0.875004\end{matrix}} \Bigr )\) | 27 | 0.098005 | \(\Bigl ({\scriptsize\begin{matrix}{} 1.124999\cr0.875001\end{matrix}} \Bigr )\) |
\((1,-1)^{\top }\) | 3 | 0.078350 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.985333\cr0\end{matrix}} \Bigr )\) | 3 | 0.079696 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.969096\cr0\end{matrix}} \Bigr )\) | 3 | 0.083422 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.952000\cr0\end{matrix}} \Bigr )\) |
\((-1,1)^{\top }\) | 1032 | 0.500529 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.575413\cr0.325587\end{matrix}} \Bigr )\) | 61 | 0.133658 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.520560\cr0.270565\end{matrix}} \Bigr )\) | 31 | 0.108214 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.462999\cr0.213001\end{matrix}} \Bigr )\) |
\((-1,-1)^{\top }\) | 1658 | 0.689241 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.249753\cr0\end{matrix}} \Bigr )\) | 107 | 0.180100 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.249991\cr0\end{matrix}} \Bigr )\) | 57 | 0.129912 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.249996\cr0\end{matrix}} \Bigr )\) |