The example proposed by Yuan et al (1988) It involves three continuous variables and four binary variables The formulation is begin aligned min x, y left(y 1 1 ight) 2 left(y 2 2 ight) 2 left(y 3 1 ight) 2 ln left(y 4 1 ight) left(x 1 1 ight) 2 left(x 2 2 ight) 2 left(x 3 3 ight) 2 end aligned subj...

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The example proposed by Yuan et al. (1988). It involves three continuous variables and four binary variables.

Question:

The example proposed by Yuan et al. (1988). It involves three continuous variables and four binary variables. The formulation is

\[\begin{aligned}& \min _{x, y}\left(y_{1}-1\right)^{2}+\left(y_{2}-2\right)^{2}+\left(y_{3}-1\right)^{2}-\ln \left(y_{4}-1\right) \\& \left(x_{1}-1\right)^{2}+\left(x_{2}-2\right)^{2}+\left(x_{3}-3\right)^{2}\end{aligned}\]

subject to

\[
\begin{aligned}
& y_{1}+y_{2}+y_{3}+x_{1}+x_{2}+x_{3} \leq 5 \\
& y_{1}^{2}+x_{1}^{2}+x_{2}^{2}+x_{3}^{2} \leq 5.5 \\
& y_{1}+x_{1} \leq 1.2 \\
& y_{2}+x_{2} \leq 1.8 \\
& y_{3}+x_{3} \leq 2.5 \\
& y_{4}+x_{1} \leq 1.2
\end{aligned}
\]

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