Superiorization of block accelerated cyclic subgradient methods

In this paper, we introduce a block version and a perturbed block version of the accelerated cyclic subgradient projections method with constraints and give their convergence analyses. The performance of the algorithm is illustrated with a numerical example from the computed tomography and six standard nonlinear test problems. We compare our algorithms with the accelerated cyclic subgradient projections method. Our algorithms produce better results than accelerated cyclic subgradient projections method and have ability to reduce the value of an objective function. Furthermore, the perturbed block version is able to control semiconvergence phenomenon comparing two other methods. © 2020 Journal of Applied and Numerical Optimization.