$\sum_{i=1}^n [2(\hat α_k[n]+\hat β_k[n])(α_k[n]+β_k[n])-(\hat α_k[n]+\hat β_k[n])^2-(α_k[n]-β_k[n])^2] \ge 4Nr, \forall k \quad (25)$
$||α_k[1]-β_k[1],...,α_k[N]-β_k[N],\frac {A_k-1}{2}|| \le \frac{A_k+1}{2},\forall k \qquad (26)$
where
$A_k=\sum_{i=1}^n [2(\hat α_k[n]+\hat β_k[n])(α_k[n]+β_k[n])-(\hat α_k[n]+\hat β_k[n])^2-(α_k[n]-β_k[n])^2] -4Nr \qquad (27)$
Click here to view the specific problem.
Solving the problem as shown in the figure, the paper mentions the transformation of (25) into its SOC form to reduce computational complexity. I'm not entirely clear on how this transformation is achieved and I hope experts in this field can offer insights.