Table 1 Influence of the step size parameters \(\beta_{n}\) and \(\lambda_{n}\) (cases 1–3) of algorithm (3.1) for different initial points
Case → | Case 1 | Case 2 | Case 3 | ||||||
|---|---|---|---|---|---|---|---|---|---|
#Initial point ↓ | Iters | Time (s) | Sol | Iters | Time (s) | Sol | Iters | Time (s) | Sol |
\((0,0)^{\top }\) | 1647 | 0.644764 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.249753\cr0\end{matrix}} \Bigr )\) | 145 | 0.210611 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.249990\cr0\end{matrix}} \Bigr )\) | 110 | 0.172755 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.249996\cr0\end{matrix}} \Bigr )\) |
\((1,1)^{\top }\) | 790 | 0.393530 | \(\Bigl ({\scriptsize\begin{matrix}{} 1.124877\cr0.875123\end{matrix}} \Bigr )\) | 51 | 0.117471 | \(\Bigl ({\scriptsize\begin{matrix}{} 1.124996\cr0.875004\end{matrix}} \Bigr )\) | 27 | 0.098625 | \(\Bigl ({\scriptsize\begin{matrix}{} 1.124997\cr0.875001\end{matrix}} \Bigr )\) |
\((1,-1)^{\top }\) | 195 | 0.231496 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.875676\cr0\end{matrix}} \Bigr )\) | 49 | 0.123486 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.795371\cr0\end{matrix}} \Bigr )\) | 36 | 0.127907 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.787096\cr0\end{matrix}} \Bigr )\) |
\((-1,1)^{\top }\) | 1069 | 0.486436 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.267956\cr0.018131\end{matrix}} \Bigr )\) | 150 | 0.207209 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.249990\cr0\end{matrix}} \Bigr )\) | 113 | 0.181702 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.249996\cr0\end{matrix}} \Bigr )\) |
\((-1,-1)^{\top }\) | 2121 | 0.847208 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.249752\cr0\end{matrix}} \Bigr )\) | 449 | 0.313106 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.249991\cr0\end{matrix}} \Bigr )\) | 361 | 0.284821 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.249996\cr0\end{matrix}} \Bigr )\) |