Sparse estimation for Cox PH models is done via Minimum approximated Information Criterion (MIC) by Su, Wijayasinghe, Fan, and Zhang (2016) <DOI:10.1111/biom.12484>. MIC mimics the best subset selection using a penalized likelihood approach yet with no need of a tuning parameter. The problem is further reformulated with a re-parameterization step so that it reduces to one unconstrained non-convex yet smooth programming problem, which can be solved efficiently. Furthermore, the re-parameterization tactic yields an additional advantage in terms of circumventing post-selection inference.
