The seamless-$L_0$ (SELO) penalty is a smooth function on $[0,\wq)$ that very  closely resembles the $L_0$ penalty, which has been  demonstrated theoretically and practically to be effective in nonconvex penalization for  variable selection. In this paper, we first generalize SELO to a class of penalties  retaining good features of SELO, and then  propose variable selection and estimation in  linear models  using the proposed  eneralized SELO (GSELO)  penalized least squares (PLS) approach.
We show that the GSELO-PLS procedure possesses the oracle property  and consistently selects the true model under some regularity conditions
in the presence of a diverging number of variables.  The entire path of GSELO-PLS estimates can  be efficiently computed through a smoothing quasi-Newton (SQN) method.
A modified BIC coupled with a continuation  strategy is developed
to select the optimal tuning parameter.
Simulation studies and analysis of a clinical data
are carried out to evaluate the finite sample performance of the
proposed method. In addition, numerical experiments
involving simulation studies and analysis of a microarray data
are also conducted for GSELO-PLS in the high-dimensional settings.