ADMM-ENK)

Although there appears to be ten additional parameters (six $\rho$’s and four $\mu$’s) in the ADMM method for ENK-SVM, we can usually set the $\rho$’s to the same value and do the same for the $\mu$’s. Hence, in practice, there is only one additional parameter to tune, and our computational experience in Section \[sec:exp\_ksvm\] is that the algorithm is fairly insensitive to the $\mu$’s and $\rho$’s.

IPM Phase
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The second phase for solving the knowledge-based SVM problem defined by (KSVM-P) follows the same steps as that described in section \[sec:ipm\]. Note that in the knowledge-based case we have decided to solve the primal problem. This decision was based on extensive numerical experiments with both the primal and dual formulation which revealed that the primal formulation is more efficient.

We found in our experiments that by introducing slack variables and transforming the above problem into a linearly equality-constrained QP, Phase 2 of HIPAD usually requires less time to solve.

HIPAD with domain knowledge incorporation
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We formally state the new two-phase algorithm for the elastic-net KSVM in Algorithm \[alg:hipad\_ksvm\].

\[alg:hipad\_ksvm\] Given ${\textbf{w}}^0, b^0, {\textbf{a}}^0, {\textbf{c}}^0, {\textbf{u}}^0,{\textbf{v}}^0,p^0,q^0,{\textbf{s}}^0\geq{\textbf{0}},{\textbf{t}}^0\geq{\textbf{0}}$. **PHASE 1: ADMM for ENK-SVM** $({\textbf{w}},b,{\textbf{u}},{\textbf{v}}) \gets $ADMM-ENK$({\textbf{w}}^0, b^0, {\textbf{a}}^0, {\textbf{c}}^0, {\textbf{u}}^0,{\textbf{v}}^0,p^0,q^0,{\textbf{s}}^0,{\textbf{t}}^0)$ **PHASE 