A Novel Approach for Updating the Penalty Parameter of Alternating Direction Method for the L1-norm Problem

An adaptive penalty update criterion for the Altering Direction Method (ADM) for solving L1 problem is presented in this paper. The criterion adjusts penalty parameters based on the primal-dual constraint function value ratios and their relative changes. A dynamic update scheme, with default settings for startup, frequency, and scaling, is developed through iterative analysis. Numerical tests indicate that the new algorithm accelerates traditional ADM and offers more flexibility for initial penalty parameter selection.