Bounded perturbation resilience and superiorization of a gradient projection alghoritm solving the convex minimization problem

Recently, a new method called superiorization has been studied in order to increase the efficiency of the algorithm, to make it less computationally demanding and to obtain more useful results than the algorithm considered for the intended application by allowing perturbations in the algorithms used in the solution of the convex optimization problem. In this thesis, our aim is to study the superiorization and perturbation resilience of the gradient projection algorithm proposed by Ertürk et al. in [1] for the solution of the convex minimization problem. In our thesis, we showed that the superiposed version of this gradient projection algorithm, which studied Erturk et al., is resistant to perturbations, thus it weakly converges to a solution of the minimization problem such as the original algorithm. We concretized our result by an example in the infinite dimensional Hilbert space. We also gave the applications of our theorem for linear inverse problems and split feasibility problems.