Before revision:  After deriving and developing this new approach, we demonstrate that (i) the ability of the  TREX heuristic to reach the global minimum is strongly dependent on the difficulty of the underlying statistical problem, (ii) the  polynomial-time algorithm for TREX permits a novel variable ranking and selection scheme, (iii) this scheme can be incorporated into a rule that controls the false discovery rate (FDR) of included features in the model.
After revision:  After deriving and developing this new approach, we demonstrate that (i) the ability of the TREX heuristic to reach the global minimum is strongly dependent on the difficulty of the underlying statistical problem, (ii) the new polynomial-time algorithm for TREX permits a novel variable ranking and selection scheme, (iii) this scheme can be incorporated into a rule that controls the false discovery rate (FDR) of included features in the model.