  From an optimizer's perspective, achieving the global optimum for a general
nonconvex problem is often provably NP-hard using the classical worst-case
analysis. In the case of Cox's proportional hazards model, by taking its
statistical model structures into account, we identify local strong convexity
near the global optimum, motivated by which we propose to use two convex
programs to optimize the folded-concave penalized Cox's proportional hazards
regression. Theoretically, we investigate the statistical and computational
tradeoffs of the proposed algorithm and establish the strong oracle property of
the resulting estimators. Numerical studies and real data analysis lend further
support to our algorithm and theory.
