Convergence Rates for the Relaxed Peaceman-Rachford Splitting Method on a Monotone Inclusion Problem

Abstract We consider the convergence behavior using relaxed Peaceman–Rachford splitting method to solve monotone inclusion problem $$0 \in (A + B)(u)$$ 0 ∈ ( A + B ) u , where $$A, B: \Re ^n \rightrightarrows ^n$$ , : ℜ n ⇉ are maximal $$\beta $$ β -strongly operators, $$n \ge 1$$ ≥ 1 and > 0$$ > . Under a technical assumption, of iterates on is proved when either A or B single-valued, fixed relaxation parameter $$\theta θ lies in interval $$(2 \beta 2 \min \{ 1/\beta \})$$ 2 min { / } With this result, we address an open that not settled Monteiro et al. (Computat Optim Appl 70:763–790, 2018) these for (2 Pointwise rate results R -linear $$[2 \{\beta [ also provided paper. Our analysis achieve atypical hence novel. Numerical experiments weighted Lasso minimization conducted test validity assumption.