We investigate the problem of finding a zero point of the sum of 3 operators where one of them is monotone Lipschitzian. We propose a new splitting method for solving this inclusion in real Hilbert spaces. The proposed framework unifies several splitting method existing in the literature. The weak convergence of the iterates is proved. The strong convergence is also obtained under an additional assumptions. Applications to sums of composite monotone inclusions and composite minimization problems are demonstrated.
We study the block coordinate forward-backward algorithm where the blocks are updated in a random and possibly parallel manner. We consider the convex case and provide a unifying analysis of the convergence under different hypotheses, advancing the state of the art in several aspects.
joint work with Minh N. Bui
We present a unifying framework for solving monotone inclusions in general Banach spaces using Bregman distances. This is achieved by introducing a new property that includes in particular the standard cocoercivity property. Several classical and recent algorithms are featured as special cases of our framework. The results are new even in standard Euclidean spaces. Applications are discussed as well.