Table 3 Influence of the step size parameters \(\beta_{n}\) and \(\lambda_{n}\) (cases 7–9) of algorithm (3.1) for different initial points
Case → | Case 7 | Case 8 | Case 9 | ||||||
|---|---|---|---|---|---|---|---|---|---|
#Initial point ↓ | Iters | Time (s) | Sol | Iters | Time (s) | Sol | Iters | Time (s) | Sol |
\((0,0)^{\top }\) | 1647 | 0.644395 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.249753\cr0\end{matrix}} \Bigr )\) | 106 | 0.167910 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.249991\cr0\end{matrix}} \Bigr )\) | 56 | 0.122966 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.249996\cr0\end{matrix}} \Bigr )\) |
\((1,1)^{\top }\) | 790 | 0.403824 | \(\Bigl ({\scriptsize\begin{matrix}{} 1.124877\cr0.875123\end{matrix}} \Bigr )\) | 51 | 0.118171 | \(\Bigl ({\scriptsize\begin{matrix}{} 1.124996\cr0.875004\end{matrix}} \Bigr )\) | 27 | 0.095997 | \(\Bigl ({\scriptsize\begin{matrix}{} 1.124999\cr0.875001\end{matrix}} \Bigr )\) |
\((1,-1)^{\top }\) | 3 | 0.080739 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.985333\cr0\end{matrix}} \Bigr )\) | 3 | 0.080157 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.969096\cr0\end{matrix}} \Bigr )\) | 3 | 0.080880 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.952000\cr0\end{matrix}} \Bigr )\) |
\((-1,1)^{\top }\) | 1032 | 0.463895 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.575413\cr0.325587\end{matrix}} \Bigr )\) | 61 | 0.133494 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.520560\cr0.270565\end{matrix}} \Bigr )\) | 31 | 0.104363 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.462999\cr0.213001\end{matrix}} \Bigr )\) |
\((-1,-1)^{\top }\) | 1658 | 0.646397 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.249753\cr0\end{matrix}} \Bigr )\) | 107 | 0.173753 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.249991\cr0\end{matrix}} \Bigr )\) | 57 | 0.127317 | \(\Bigl ({\scriptsize\begin{matrix}{} 0.249996\cr0\end{matrix}} \Bigr )\) |