2025/11/18 by Qin, Liqian, Gibali, Aviv, Zhang, Cuijie +1
#47H05 #65K15 #90C25 #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2511.14050
In this paper, we introduce three novel splitting algorithms for solving structured monotone inclusion problems involving the sum of a maximally monotone operator, a monotone and Lipschitz continuous operator and a cocoercive operator. Each proposed method extends one of the classical schemes: the semi-forward-reflected-backward splitting algorithm, the semi-reflected-forward-backward splitting algorithm, and the outer reflected forward-backward splitting algorithm by incorporating a nonlinear momentum term. Under appropriate step-size conditions, we establish the weak convergence of all three algorithms, and further prove their R-linear convergence rates under strong monotonicity assumptions. Preliminary numerical experiments on both synthetic datasets and real-world quadratic programming problems in portfolio optimization demonstrate the effectiveness and superiority of the proposed algorithms.