An adaptive splitting algorithm for the sum of two generalized monotone operators and one cocoercive operator

Abstract Splitting algorithms for finding a zero of sum operators often involve multiple steps which are referred to as forward or backward steps. Forward the explicit use and implicitly via their resolvents. In this paper, we study an adaptive splitting algorithm three operators. We assume that two generalized monotone resolvents computable, while other operator is cocoercive but its resolvent missing costly compute. Our adapts new parameters monotonicity and, at same time, combines appropriate guarantee convergence solution problem.