The Linearized Bregman Method via Split Feasibility Problems: Analysis and Generalizations
This work provides a theoretical extension for sparse optimization methods, but it is incremental as it builds on existing linearized Bregman techniques.
The paper tackled the problem of computing sparse solutions to linear equations by reformulating it as a split feasibility problem, proposing a Bregman projection-based algorithmic framework with proven convergence, and generalizing it to handle other objectives, incremental iterations, non-Gaussian noise, and box constraints.
The linearized Bregman method is a method to calculate sparse solutions to systems of linear equations. We formulate this problem as a split feasibility problem, propose an algorithmic framework based on Bregman projections and prove a general convergence result for this framework. Convergence of the linearized Bregman method will be obtained as a special case. Our approach also allows for several generalizations such as other objective functions, incremental iterations, incorporation of non-gaussian noise models or box constraints.