  We propose algorithms to take point sets for kernel-based interpolation of
functions in reproducing kernel Hilbert spaces (RKHSs) by convex optimization.
We consider the case of kernels with the Mercer expansion and propose an
algorithm by deriving a second-order cone programming (SOCP) problem that
yields $n$ points at one sitting for a given integer $n$. In addition, by
modifying the SOCP problem slightly, we propose another sequential algorithm
that adds an arbitrary number of new points in each step. Numerical experiments
show that in several cases the proposed algorithms compete with the $P$-greedy
algorithm, which is known to provide nearly optimal points.
