A new active zero set descent algorithm for least absolute deviation with generalized LASSO penalty

A new active zero set descent algorithm is proposed for least absolute deviation (LAD) problems with generalized LASSO penalty. Zero set contains the terms in the cost function that are zero-valued at the solution. Unlike state-of-art numerical approximation strategies such as interior point method, user-chosen threshold value is not required by the proposed algorithm to identify the zero set. Moreover, no nested iteration is needed. The algorithm updates the zero set and basis search directions recursively until optimality conditions are satisfied. It is also shown that the proposed algorithm converges in finitely many steps. Extensive simulation studies and real data analysis are conducted to confirm the time-efficiency of our algorithm.