Step  1. Initialization. Let and pick , set .
Step  2. Predictor. Let
      ,     (*)
and
          .                (**)
Step  3. If the stepsizes and are chosen satisfying
          ,                  (#)
then go to Step 4. Otherwise, increase and go back to Step 2.
Step  4. Corrector and updating
          .                ($)
Step  5. Adjustment
   .
Set .
Algorithm 1: General primal-dual relaxed-PPA method.