Quantitative results for a Tseng-type primal-dual method for composite monotone inclusions

Abstract We provide quantitative results on a seminal Tseng-type primal-dual splitting algorithm for solving monotone inclusions due to Combettes and Pesquet which involves a mixture of sums, linear compositions and parallel sums of set-valued and Lipschitzian operators. For that, we first give quantitative results on a version of Tseng’s forward-backward-forward splitting algorithm including error terms and variable parameters, partially extending previous work of Treusch and Kohlenbach, to which the method of Combettes and Pesquet is then reduced.