  For solving structured monotone inclusion problems involving the sum of
finitely many maximal monotone operators, we propose and study a relative-error
inertial-relaxed inexact projective splitting algorithm. The proposed algorithm
benefits from a combination of inertial and relaxation effects, which are both
controlled by parameters within a certain range. We propose sufficient
conditions on these parameters and study the interplay between them in order to
guarantee weak convergence of sequences generated by our algorithm.
Additionally, the proposed algorithm also benefits from inexact subproblem
solution within a relative-error criterion. Illustrative numerical experiments
on LASSO problems indicate some improvement when compared with previous
(noninertial and exact) versions of projective splitting.
