Four-Operator Splitting via a Forward–Backward–Half-Forward Algorithm with Line Search

In this article, we provide a splitting method for solving monotone inclusions in real Hilbert space involving four operators: maximally monotone, monotone-Lipschitzian, cocoercive, and monotone-continuous operator. The proposed takes advantage of the intrinsic properties each operator, generalizing forward–backward–half-forward Tseng’s algorithm with line search. At iteration, our defines step size by using search which monotone-Lipschitzian cocoercive operators need only one activation. We also derive nonlinearly constrained composite convex optimization problems spaces. Finally, implement least-square problem compare its performance available methods literature.