Focus of this work is solving a non-smooth constraint minimization problem by a primal-dual splitting algorithm involving proximity operators. The problem is penalized by the Bregman divergence associated with the non-smooth total variation (TV) functional. We analyze two aspects: Firstly, the convergence of the regularized solution of the minimization problem to the minimum norm solution. Second, the convergence of the iteratively regularized minimizer to the minimum norm solution by a primal-dual algorithm. For both aspects, we use the assumption of a variational source condition (VSC). This work emphasizes the impact of the choice of the parameters in stabilization of a primal-dual algorithm. Rates of convergence are obtained in terms of some concave, positive definite index function. The algorithm is applied to a simple two-dimensional image processing problem. Sufficient error analysis profiles are provided based on the size of the forward operator and the noise level in the measurement.

这项工作的重点是通过涉及邻近算子的原始对偶拆分算法解决非平滑约束最小化问题。与不平滑的总变化（TV）函数相关的Bregman散度使该问题受到惩罚。我们分析两个方面：首先，最小化问题的正则解与最小范数解的收敛。其次，通过原始对偶算法将迭代正则化的最小化器收敛到最小范数解。对于这两个方面，我们都使用可变源条件（VSC）的假设。这项工作强调了参数选择对原始对偶算法稳定的影响。收敛速度是根据一些凹的正定指数函数获得的。该算法应用于简单的二维图像处理问题。根据前向操作员的大小和测量中的噪声水平，提供了足够的错误分析配置文件。