We investigate the techniques and ideas used in the convergence analysis of two proximal ADMM algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the ADMM algorithm that is able to handle convex optimization problems involving an additional smooth function in its objective, and which is evaluated through its gradient. Moreover, in each iteration we allow the use of variable metrics, while the investigations are carried out in the setting of infinite dimensional Hilbert spaces. This algorithmic scheme is investigated from the point of view of its convergence properties.
翻译:我们调查了在对两种最接近ADMM算法进行趋同分析时所使用的技术和想法,这些算法用于解决线性操作员构成的松动优化问题。此外,我们还制定了ADMM算法的变体,能够处理涉及目标中额外平稳功能的松动优化问题,并通过其梯度进行评估。此外,在每一次迭代中,我们允许使用可变量度量,而调查则在无限的维度希尔伯特空间设置中进行。这一算法方案从其趋同性的角度加以调查。