Fitting sparse linear models under the sufficient and necessary condition for model identification

We propose an enhanced support detection and root finding approach (ESDAR) to variable selection in sparse linear models. ESDAR is motivated from the KKT conditions for ?0 penalized regression. In ESDAR, we introduce a step size balance primal dual variables determining of solution. establish sharp oracle error bound recovery property solution sequence generated by under weakest possible condition on design matrix that sufficient necessary model be identifiable. The results obtained are weaker than those Lasso concave methods including SCAD MCP literature.