Towards split monotone inclusions with composite operators: a regularization approach

Relying on the Yosida approximate, we present an algorithmic approach for nding solutions of split monotone problems involving the composite of a monotone operator and a bounded linear mapping. The proposed algorithms can be used for solving problems arising in image processing and in location theory. Convergence results are provided and some remarks on potential developments based on the variational composition, whose utility was demonstrated in [1] by applications to the theory of measurable multifunctions and elliptic PDEs with singular coecients, are stated.