  Monotone inclusions play an important role in studying various convex
minimization problems. In this paper, we propose a forward-partial
inverse-half-forward splitting (FPIHFS) algorithm for finding a zero of the sum
of a maximally monotone operator, a monotone Lipschitzian operator, a
cocoercive operator, and a normal cone of a closed vector subspace. The FPIHFS
algorithm is derived from a combination of the partial inverse method with the
forward-backward-half-forward splitting algorithm. As applications, we employ
the proposed algorithm to solve several composite monotone inclusions problems,
which include a finite sum of maximally monotone operators and parallel-sum of
operators. In particular, we obtain a primal-dual splitting algorithm for
solving a composite convex minimization problem, which has wide applications in
many real problems. To verify the efficiency of the proposed algorithm, we
apply it to solve the Projection on Minkowski sums of convex sets problem and
the generalized Heron problem. Numerical results demonstrate the effectiveness
of the proposed algorithm.
