  In the rapidly evolving internet-of-things (IoT) ecosystem, effective data
analysis techniques are crucial for handling distributed data generated by
sensors. Addressing the limitations of existing methods, such as the
sub-gradient approach, which fails to distinguish between active and non-active
coefficients effectively, this paper introduces the decentralized smoothing
alternating direction method of multipliers (DSAD) for penalized quantile
regression. Our method leverages non-convex sparse penalties like the minimax
concave penalty (MCP) and smoothly clipped absolute deviation (SCAD), improving
the identification and retention of significant predictors. DSAD incorporates a
total variation norm within a smoothing ADMM framework, achieving consensus
among distributed nodes and ensuring uniform model performance across disparate
data sources. This approach overcomes traditional convergence challenges
associated with non-convex penalties in decentralized settings. We present
theoretical proofs and extensive simulation results to validate the
effectiveness of the DSAD, demonstrating its superiority in achieving reliable
convergence and enhancing estimation accuracy compared with prior methods.
