The Linearized Bregman Method via Split Feasibility Problems: Analysis and Generalizations
The Linearized Bregman Method via Split Feasibility Problems: Analysis and Generalizations
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DOI：
10.1137/130936269
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发表时间：
2013-09
期刊：
影响因子：
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通讯作者：
D. Lorenz;F. Schöpfer;S. Wenger
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文献类型：
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作者：
D. Lorenz;F. Schöpfer;S. Wenger
线性化布雷格曼方法是一种计算线性方程组稀疏解的方法。我们将这个问题表述为一个分裂可行性问题，提出了一个基于Bregman投影的算法框架，并证明了该框架的一般收敛结果。作为一种特殊情况，将得到线性化Bregman方法的收敛性。我们的方法还允许一些推广，如其他目标函数，增量迭代，非高斯噪声模型或盒约束的合并。
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.