A globally convergent hybrid-adaptive accelerated Douglas–Rachford splitting method for absolute value equations

In this paper, we propose a hybrid-adaptive accelerated Douglas–Rachford splitting method (HAA-DRSM) for solving absolute value equations of the form Ex−|x|−p=0. Unlike existing inertial acceleration techniques, HAA-DRSM employs a hybrid strategy that combines convex combination, inertial extrapolation, and adaptive regulation. By leveraging multiple past iterates, it generates the inertial point via two distinct alternating schemes. Under mild assumptions, including ‖E−1‖≤1, we establish global convergence and convergence-rate results for HAA-DRSM. Numerical experiments are conducted to demonstrate the effectiveness and competitiveness of HAA-DRSM.