## 4 Numerical Results
\begin{table}
\begin{tabular}{c c c c c c} \hline \(p\) & \(\mathbf{k}\) & \(\boldsymbol{x_{k}}\) & \(\boldsymbol{\theta(z_{k})}\) & \(\boldsymbol{\Psi(x_{k})}\) & \(\boldsymbol{2x_{1}^{k}+3x_{2}^{k}}\) \\ \hline
2 & \(10^{3}\) & \((42.6799,15.7988,0,0.2833,0.4704)\) & 5.3426 & 5.1369 & 132.7562 \\
2 & \(10^{4}\) & \((42.5951,15.8259,0,0.2826,0.4706)\) & 5.2120 & 5.0197 & 132.6679 \\
2 & \(10^{5}\) & \((41.9961,16.0177,0.2773,0.4752)\) & 4.3428 & 4.2083 & 132.0453 \\
4 & \(10^{3}\) & \((42.7005,15.7755,0,0,2.846,0.4717)\) & 23.7543 & 5.1012 & 132.7276 \\
4 & \(10^{4}\) & \((42.6135,15.8036,0,0.2826,0.4707)\) & 5.2027 & 5.0096 & 132.6377 \\
4 & \(10^{5}\) & \((41.9980,16.0049,0.2772,0.4753)\) & 4.3207 & 4.1872 & 132.0108 \\
6 & \(10^{3}\) & \((42.7599,15.7531,0,0.2838,0.4686)\) & 55.2438 & 5.2217 & 132.7789 \\
6 & \(10^{4}\) & \((42.6568,15.7867,0,0.2829,0.4703)\) & 5.2612 & 5.0652 & 132.6738 \\
6 & \(10^{5}\) & \((42.0153,15.9977,0,0.2773,0.4753)\) & 4.3411 & 4.2060 & 132.0235 \\ \hline \end{tabular}
\end{table} 
Table 6: Numerical results for Example 3 based on Condition 2. \begin{table}
\begin{tabular}{c c c c c c} \hline \(p\) & \(\mathbf{k}\) & \(\boldsymbol{x_{k}}\) & \(\boldsymbol{\theta(z_{k})}\) & \(\boldsymbol{\Psi(x_{k})}\) & \(\boldsymbol{2x_{1}^{k}+3x_{2}^{k}}\) \\ \hline
2 & \(10^{3}\) & \((42.6730,15.8000,0,0.2848,0.4688)\) & 18.1932 & 5.1078 & 132.7462 \\
2 & \(10^{4}\) & \((42.6057,15.8216,0,0.2844,0.4694)\) & 5.2138 & 5.0089 & 132.6760 \\
2 & \(10^{5}\) & \((42.0369,16.0037,0,0.2791,0.4740)\) & 4.3894 & 4.2424 & 132.0850 \\
4 & \(10^{3}\) & \((42.7120,15.7720,0,0.2872,0.4829)\) & 1999.1 & 5.3083 & 132.7399 \\
4 & \(10^{4}\) & \((42.6301,15.7986,0,0.2844,0.4694)\) & 5.2164 & 5.0103 & 132.6559 \\
4 & \(10^{5}\) & \((42.0487,15.9888,0,0.2791,0.4740)\) & 4.3826 & 4.2359 & 132.0628 \\
6 & \(10^{3}\) & \((42.7277,15.7628,0,0.2853,0.4687)\) & 5.3534 & 5.1372 & 132.7438 \\
6 & \(10^{4}\) & \((42.6539,15.7870,0,0.2846,0.4692)\) & 5.2433 & 5.0360 & 132.6688 \\
6 & \(10^{5}\) & \((42.0594,15.9826,0,0.2791,0.4740)\) & 4.3925 & 4.2458 & 132.0667 \\ \hline \end{tabular}
\end{table} 
Table 5: Numerical results for Example 3 based on Condition 1. In the following part of this subsection, we give a large-scale stochastic linear complementarity problem named the stochastic Murty problem. When \(\Omega=\{\omega|\omega=\frac{1}{2}\}\), the large-scale stochastic linear complementarity problem reduces to the Murty problem, which is intensively studied in [25; 26; 27; 28; 29]. **Example 4**: _(Stochastic Murty problem) Consider \(SACP(M(\omega),q(\omega))\) with:_  
\[M(\omega)=\left( \begin{array}{cccc}\frac{1}{2}+\omega&2&\cdots&2\\ 0&\frac{1}{2}+\omega&\cdots&2\\ \vdots&\vdots&\ddots&\\ 0&\cdots&\frac{1}{2}+\omega\end{array} \right),q(\omega)=\left( \begin{array}[] {c}-\frac{3}{2}+\omega\\ -\frac{3}{2}+\omega\\ \vdots\\ -\frac{3}{2}+\omega\end{array} \right),\]  
_where \(M(\omega)\in\Re^{n\times n},q(\omega)\in\Re^{n}.\)\(\Omega=\{\omega_{1},\omega_{2}\}=\{0,1\},\) and \(p_{i}=P(\omega_{i}\in\Omega)=0.5,i=1,2.\)_  
In Table 7, we give the comparison of Method 1 with the SQP method in the fmincon tool box, when the dimensions of Example 4 are 10, 100, 200, 300 and 400; where \(\theta(x,y)=\frac{1}{2}\|F(x,y)\|^{2}.\)\(x_{0}\) are chosen randomly in \(\Re^{n}.\)\(y_{0}\) are chosen randomly in \(\Re^{2n}\), \(\lambda=0.0001.\)  
**Remark 2**: _By the numerical results of Example 4, we can see that Method 1 is very suitable to solve large-scale SLCP. Moreover, Method 1 can be used flexible by adjusting the value of \(p.\)_