Let $f(x) = \sum_{i=1}^n \alpha_ik(x,x_i) + \alpha_0$ for some kernel $k$. I want to show that there exists a kernel such that the solutions to the following optimization problems are the same:
$$\text{min}_{\alpha, \alpha_0} \sum_{i=1}^n[1-y_if(x_i)]_+ + \frac{\lambda}{2}\alpha^TK\alpha $$
and
$$\text{min}_{\alpha, \alpha_0} \sum_{i=1}^n[1-y_if(x_i)]_+ + \frac{\lambda}{2}\alpha^T\alpha $$
where $K_{ij} = k(x_i, x_j)$ and $\alpha = (\alpha_1, ..., \alpha_n)^T$ and $\lambda > 0$. This is problem 12.2 of Elements of Statistical Learning by Tibshirani et. al. I have zero ideas of where to start. Any help would be greatly appreciated.