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