Table 4 An algorithm for the meta-analytic SVM via Newton’s method

Step 1: For 1≤m≤M, set the initial value \(\beta ^{(m)^{(0)}}\).

Step 2: Set t=0 and minimize \(\tilde {Q}^{\lambda _{1},\lambda _{2}}\left (\beta _{j}^{(m)}\right)\) via Newton’s method:

\(\beta _{j}^{(m)^{(t+1)}} \leftarrow \beta _{j}^{(m)^{(t)}} - \frac {\nabla \tilde {Q}^{\lambda _{1},\lambda _{2}} \left (\beta _{0}^{(m)^{(t+1)}}, \ldots, \beta _{j-1}^{(m)^{(t+1)}}, \beta _{j}^{(m)^{(t)}}, \ldots, \beta _{p}^{(m)^{(t)}}\right)_{j+1}} {\nabla ^{2} \tilde {Q}^{\lambda _{1},\lambda _{2}} \left (\beta _{0}^{(m)^{(t+1)}}, \ldots, \beta _{j-1}^{(m)^{(t+1)}}, \beta _{j}^{(m)^{(t)}}, \ldots, \beta _{p}^{(m)^{(t)}}\right)_{j+1,j+1}}\)

for 0≤j≤p and 1≤m≤M.

Step 3: Update t=t+1 and go to Step 2 until convergence.