# Properties of the Quadratic Transformation of Dual Variables
## 6 Solving Test Problems
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & \(\Delta\psi\) & \(\Delta f\) & \
\begin{tabular}{c} **Number of** \\ **Iterations** \\ \end{tabular} &
\begin{tabular}{c} **Number of Evaluations** \\ **of Function and** \\ **Gradient** \\ \end{tabular} \\ \hline \multicolumn{5}{c}{Function LP\_R\_Y2 \(mb=50\), \(ma=25\), \(md=25\)} \\ sub & \(3.134\times 10^{-8}\) & \(3.134\times 10^{-8}\) & 971 & 1907 \\ Shor & \(4.980\times 10^{-1}\) & \(1.706\times 10^{-5}\) & 2495 & 4554 \\ Orty & \(5.280\times 10^{-10}\) & \(3.259\times 10^{-10}\) & 1864 & 3535 \\ yv & \(4.952\times 10^{-9}\) & \(3.044\times 10^{-9}\) & 507 & 1037 \\ MsgrPPR & \(5.002\times 10^{-1}\) & \(3.355\times 10^{-6}\) & 126 & 319 \\ BFGS & \(2.701\times 10^{-1}\) & \(7.262\times 10^{-11}\) & 656 & 1524 \\ \multicolumn{5}{c}{Function LP\_R\_Y1 \(mb=50\), \(ma=25\), \(md=25\)} \\ sub & \(4.980\times 10^{-1}\) & \(6.439\times 10^{-3}\) & 1280 & 2540 \\ Shor & \(4.980\times 10^{-1}\) & \(2.210\times 10^{-6}\) & 2972 & 6250 \\ Orty & \(4.980\times 10^{-1}\) & \(2.057\times 10^{-6}\) & 1179 & 2189 \\ yv & \(4.980\times 10^{-1}\) & \(7.798\times 10^{-6}\) & 1121 & 2087 \\ \multicolumn{5}{c}{Function L2\_Y2 \(mb=50\), \(ma=25\), \(md=25\)} \\ sub & \(3.967\times 10^{-10}\) & \(4.126\times 10^{-5}\) & 178 & 371 \\ Shor & \(1.065\times 10^{-12}\) & \(1.988\times 10^{-5}\) & 2481 & 4541 \\ Orty & \(5.418\times 10^{-12}\) & \(3.259\times 10^{-5}\) & 909 & 1772 \\ yv & \(8.057\times 10^{-11}\) & \(1.533\times 10^{-5}\) & 284 & 609 \\ MsgrPPR & \(2.745\times 10^{-5}\) & \(4.235\times 10^{-3}\) & 58 & 151 \\ BFGS & \(2.865\times 10^{-13}\) & \(8.488\times 10^{-6}\) & 439 & 966 \\ \multicolumn{5}{c}{Function L2\_Y1 \(mb=50\), \(ma=25\), \(md=25\)} \\ sub & \(2.252\times 10^{-7}\) & \(9.320\times 10^{-3}\) & 2221 & 4269 \\ Shor & \(5.502\times 10^{-11}\) & \(4.765\times 10^{-6}\) & 2780 & 5871 \\ Orty & \(3.657\times 10^{-15}\) & \(4.047\times 10^{-7}\) & 2589 & 4639 \\ yv & \(5.850\times 10^{-12}\) & \(1.390\times 10^{-6}\) & 1668 & 3208 \\ \multicolumn{5}{c}{Function 1/\(\chi\_Y2 \(mb=50\), \(ma=25\), \(md=25\)} \\ sub & \(2.771\times 10^{-13}\) & \(1.434\times 10^{-8}\) & 130 & 267 \\ Shor & \(5.433\times 10^{-13}\) & \(2.314\times 10^{-8}\) & 71 & 149 \\ Orty & \(1.521\times 10^{-12}\) & \(1.813\times 10^{-7}\) & 193 & 399 \\ yv & \(2.544\times 10^{-15}\) & \(1.207\times 10^{-9}\) & 84 & 167 \\ MsgrPPR & \(3.782\times 10^{-15}\) & \(8.183\times 10^{-9}\) & 41 & 90 \\ BFGS & \(9.539\times 10^{-15}\) & \(1.098\times 10^{-8}\) & 86 & 181 \\ Function 1/\(\chi\_Y1 \(mb=50\), \(ma=25\), \(md=25\) & & & \\ sub & \(5.754\times 10^{-8}\) & \(3.910\times 10^{-7}\) & 218 & 441 \\ Shor & \(3.289\times 10^{-4}\) & \(8.393\times 10^{-5}\) & 622 & 1340 \\ Orty & \(7.004\times 10^{-5}\) & \(2.455\times 10^{-5}\) & 289 & 512 \\ yv & \(1.760\times 10^{-4}\) & \(5.199\times 10^{-5}\) & 221 & 416 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results of calculations for dimensions \(n=10,000\), \(m=250\) with \(mb=50\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & \(\Delta\psi\) & \(\Delta f\) & \
\begin{tabular}{c} **Number of** \\ **Terations** \\ \end{tabular} &
\begin{tabular}{c} **Number of Evaluations** \\ **of Function and** \\ **Gradient** \\ \end{tabular} \\ \hline \multicolumn{5}{c}{Function LP\_R\_Y2 \(mb=50\), \(ma=25\), \(md=25\)} \\ sub & \(5.050\times 10^{-1}\) & \(6.241\times 10^{-3}\) & 139 & 284 \\ Shor & \(5.050\times 10^{-1}\) & \(1.594\times 10^{-5}\) & 1926 & 3767 \\ Orty & \(5.050\times 10^{-1}\) & \(1.493\times 10^{-5}\) & 335 & 693 \\ vv & \(5.050\times 10^{-1}\) & \(2.622\times 10^{-6}\) & 181 & 348 \\ MsgrPPR & \(5.079\times 10^{-1}\) & \(1.973\times 10^{-3}\) & 200 & 448 \\ BFGS & \(5.050\times 10^{-1}\) & \(1.464\times 10^{-5}\) & 286 & 665 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Results of calculations for dimensions \(n=5000\), \(m=500\) with \(mb=50\). The performed computer experiment confirms the efficiency of the quadratic transformation.