# Closest Farthest Widest
## 4 Numerical Experiments
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Set** & **Dimension** & **Type** & **Homotopy** & **Fraction** & **Maximum** & **Seconds** \\ \hline L1 ball & 2 & widest & no & 1.0 & 2.0 & 0.0764 \\ L1 ball & 2 & widest & yes & 1.0 & 2.0 & 0.0761 \\ elastic net & 2 & farthest & no & & 2.2883 & 0.113 \\ elastic net & 2 & widest & no & 1.0 & 1.4641 & 0.0818 \\ elastic net & 2 & widest & yes & 1.0 & 1.4641 & 0.277 \\ box & 3 & farthest & no & & 3.9572 & 0.0472 \\ box & 3 & widest & no & 1.0 & 3.4641 & 0.0458 \\ box & 3 & widest & yes & 1.0 & 3.4641 & 0.0651 \\ ball \(\cap\) orthant & 3 & farthest & no & & 3.2791 & 0.0443 \\ ball \(\cap\) orthant & 3 & widest & no & 0.78 & 1.4142 & 0.0436 \\ simplex & 3 & farthest & no & & 3.0727 & 0.045 \\ simplex & 3 & widest & no & 1.0 & 1.4142 & 0.0461 \\ simplex & 3 & widest & yes & 1.0 & 1.4142 & 0.0763 \\ L1 ball & 3 & farthest & no & & 3.0727 & 0.0439 \\ L1 ball & 3 & widest & no & 1.0 & 2.0 & 0.0465 \\ L1 ball & 3 & widest & yes & 1.0 & 2.0 & 0.0671 \\ elastic net & 3 & farthest & no & & 2.8509 & 0.0705 \\ elastic net & 3 & widest & no & 1.0 & 1.4641 & 0.0489 \\ elastic net & 3 & widest & yes & 1.0 & 1.4641 & 0.249 \\ box & 10 & farthest & no & & 5.6758 & 0.0475 \\ box & 10 & widest & no & 1.0 & 6.3246 & 0.0454 \\ box & 10 & widest & yes & 1.0 & 6.3246 & 0.0612 \\ ball \(\cap\) orthant & 10 & farthest & no & & 3.6022 & 0.043 \\ ball \(\cap\) orthant & 10 & widest & no & 1.0 & 1.4142 & 0.0449 \\ ball \(\cap\) orthant & 10 & widest & yes & 1.0 & 1.4142 & 0.0449 \\ simplex & 10 & widest & yes & 1.0 & 1.4142 & 0.0442 \\ simplex & 10 & widest & yes & 1.0 & 1.4142 & 0.0797 \\ L1 ball & 10 & farthest & no & & 3.2937 & 0.0434 \\ L1 ball & 10 & widest & no & 1.0 & 2.0 & 0.0427 \\ L1 ball & 10 & widest & yes & 1.0 & 2.0 & 0.0696 \\ elastic net & 10 & farthest & no & & 3.1077 & 0.0496 \\ elastic net & 10 & widest & no & 1.0 & 1.4641 & 0.0537 \\ elastic net & 10 & widest & yes & 1.0 & 1.4641 & 0.328 \\ box & 1000 & farthest & no & & 59.61 & 0.0444 \\ box & 1000 & widest & no & 1.0 & 63.246 & 0.0505 \\ box & 1000 & widest & yes & 1.0 & 63.246 & 0.175 \\ ball \(\cap\) orthant & 1000 & farthest & no & & 31.962 & 0.0425 \\ ball \(\cap\) orthant & 1000 & widest & no & 1.0 & 1.4142 & 0.0447 \\ ball \(\cap\) orthant & 1000 & widest & yes & 1.0 & 1.4142 & 0.0447 \\ simplex & 1000 & farthest & no & & 31.325 & 0.0456 \\ simplex & 1000 & widest & no & 1.0 & 1.4142 & 0.046 \\ simplex & 1000 & widest & yes & 1.0 & 1.4142 & 0.048 \\ L1 ball & 1000 & widest & no & 1.0 & 2.0 & 0.0445 \\ elastic net & 1000 & farthest & no & & 31.3 & 0.523 \\ elastic net & 1000 & widest & no & 1.0 & 1.4641 & 0.277 \\ elastic net & 1000 & widest & yes & 1.0 & 1.4641 & 0.277 \\ elastic net & 1000 & widest & yes & 1.0 & 1.4641 & 0.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Evaluation of the projected gradient ascent algorithms. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Set** & **Dimension** & **Type** & **Homotopy** & **Fraction** & **Maximum** & **Seconds** \\ \hline box & 2 & farthest & no & & 2.9624 & 0.802 \\ box & 2 & widest & no & 1.0 & 2.8284 & 0.0291 \\ box & 2 & widest & yes & 0.99 & 2.8284 & 0.129 \\ ball \(\cap\) orthant & 2 & farthest & no & & 2.5994 & 0.128 \\ ball \(\cap\) orthant & 2 & widest & no & 0.78 & 1.0 & 0.0278 \\ ball \(\cap\) orthant & 2 & widest & yes & 0.51 & 1.4142 & 0.09 \\ simplex & 2 & farthest & no & & 2.5465 & 0.761 \\ simplex & 2 & widest & no & 1.0 & 1.4142 & 0.0259 \\ simplex & 2 & widest & yes & 0.7 & 1.4142 & 0.0906 \\ L1 ball & 2 & farthest & no & & 2.5465 & 0.154 \\ L1 ball & 2 & widest & no & 1.0 & 2.0 & 0.0273 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._