2: IPM for KSVM** $\widetilde{{\textbf{w}}} \gets $ non-zero components of ${\textbf{w}}$ $(\widetilde{X}, \widetilde{Y}) \gets $ sub-matrices of $(X, Y)$ corresponding to the support of ${\textbf{w}}$ $\eta_u^0 \gets {\textbf{d}}^T{\textbf{u}}-b+1$ $\eta_v^0 \gets {\textbf{g}}^T{\textbf{v}}+b+1$ $({\textbf{w}},b) \gets \textrm{SVM-IPM}$$(\widetilde{X}, \widetilde{Y}, \widetilde{{\textbf{w}}},b,{\textbf{u}},{\textbf{v}},\eta_u^0,\eta_v^0$) $({\textbf{w}},b)$

Numerical results
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We present our numerical experience with the two main algorithms proposed in this paper: HIPAD and its knowledge-based version HIPAD-ENK. We compare their performance with their non-hybrid counterparts, i.e., ADMM-ENSVM and ADMM-ENK, which use ADMM to solve the original SVM problem. The transition condition at the end of Phase 1 is specified in (\[eq:hipad\_transition\]), with $\epsilon_{tol} = 10^{-2}$. The stopping criteria for ADMM are as follows: $\frac{|F^{k+1}-F^k|}{\max\{1,|F^k|\}} \leq \epsilon_1, \|{\textbf{a}}-({\textbf{e}}-\bar{X}{\textbf{w}}-{\textbf{y}}b)\|_2\leq \epsilon_1, \|{\textbf{c}}-{\textbf{w}}\|_2\leq \epsilon_1$ and $ \frac{\|{\textbf{w}}^{k+1}-{\textbf{w}}\|_2}{\|{\textbf{w}}^k\|_2} \leq \epsilon_2$, with $\epsilon_1 = 10^{-5}$, and $\epsilon_2 = 10^{-3}$.

HIPAD vs ADMM
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To demonstrate the practical effectiveness of HIPAD, we tested the algorithm on nine real data sets which are publicly available. **rcv1** [@lewis2004rcv1] is a collection of manually categorized news wires from Reuters. The original multiple labels have been consolidated into two classes for binary classification. **real-sim** contains UseNet articles from four discussion groups, for simulated auto racing, simulated aviation, real autos, and real aviation. Both **rcv1** and **real-sim** have large 