Modified alternating direction methods for the modified multiple-sets split feasibility problems
The authors present three modified alternative direction methods (ADMs) for solving two new multiple-sets split feasibility problem (MSFP) models. The first model is more separable than the original one, which enables one to apply a modified ADM with parallel feature to solve it. Then, to overcome the difficulty of computing projections onto the constraint sets, a special version of this modified method with the strategy of projections onto a half-space is given. The second model consists in finding a least Euclidean norm solution of the MSFP, for which another modified ADM is provided. Comparing it with some algorithms, the efficiency of these methods is shown in preliminary computational tests. These parallel methods are implemented in a personal computer without parallel-architecture. If the methods are implemented in a parallel computer, they may have a higher convergent speed.
scientific article; zbMATH DE number 6363604
scientific article