An inertial Mann forward-backward splitting algorithm of variational inclusion problems and its applications - Peeyada, Pronpat; Suparatulatorn, Raweerote; Cholamjiak, Watcharaporn (Chaos, solitons and fractals, 2022)
In this paper, we introduce the inertial Mann forward-backward splitting algorithm for solving variational inclusion problem of the sum of two operators, the one is maximally monotone and the other is monotone and Lipschitz continuous. Under standard assumptions, we prove the weak convergence theorem of the proposed algorithm. We show that the algorithm is flexible to use by choosing the variable stepsizes and two different algorithms are shown by choosing constant stepsize and update stepsize. Moreover, we apply our algorithms to solve data classification using the Wisconsin original breast cancer data set as a training set. We also compare our algorithms with the other two algorithms to show the efficiency of the algorithm and show suitably learns the training dataset and generalizes well to a hold-out dataset of the algorithm by considering overfitting. Finally, we apply our algorithms to solve signal recovery and show the efficiency of the algorithm by compare with the other two algorithms. The results of data classification and signal recovery showed that choosing the right stepsizes of the algorithm would be a good efficient for the different problems. 46T99, 47B02, 47H05, 47J25, 49M37. •The paper proposed an advanced forward-backward splitting algorithm in combination with an inertial technique and Mann algorithm for solving variational inclusion problems.•The weak convergence result has been established in Hilbert spaces subject to certain conditions.•It developed an application to predict breast cancer through the proposed algorithm.•It used breast cancer Wisconsin original data set as a training set to show efficiency of the newly developed algorithm by comparing with two other algorithms in term of three key parameters viz. accuracy, recall and precision.•It developed an application to signal recovery and showed the efficiency of the algorithm by comparing with the other two algorithms.