Strengthened splitting methods for computing resolvents

In this work, we develop a systematic framework for computing the resolvent of sum two or more monotone operators which only activates each operator in individually. The key tool development is notion “strengthening” set-valued operator, can be viewed as type regularisation that preserves computational tractability. After deriving number iterative schemes through framework, demonstrate their application to best approximation problems, image denoising and elliptic PDEs.