Abstract: As machine learning algorithms continue to evolve and incorporate more features, effective variable selection has become a critical issue. To control the false discovery rate of regression coefficients in the variable selection, Bogdan et al. proposed the SLOPE model in 2015, which considers a linear regression model regularized by the OWL1 norm. In this paper, we consider a new regression model that uses an OWL1 norm constraint, enabling more flexible control of the false discovery rate through two parameters, $\lambda$ and $\tau$. We designed a fast algorithm that efficiently solves this model by using the dual semismooth Newton based proximal point algorithm (PPDNA). The algorithm's outer layer uses the proximal point algorithm, while the inner layer employs the semismooth Newton method to solve the subproblems efficiently. Meanwhile, the special structure of the generalized Jacobian induced by the projector onto the OWL1 norm ball is exploited to efficiently handle the corresponding Newton linear systems in the inner algorithm. Finally, we demonstrate the effectiveness and robustness of PPDNA by comparing it with two popular algorithms using both simulated data and large-scale real datasets.

Key words: OWL1 norm, semismooth Newton method, proximal point method