We present a computational study of effectiveness of declarative approaches for three optimization problems in the realm of abstract argumentation. In the largest extension problem, the task is to compute a σ-extension of largest cardinality (rather than, e.g., a subset-maximal extension) among the σ-extensions of a given argumentation framework (AF). The two other problems considered deal with a form of dynamics in AFs: given a subset S of arguments of an AF, the task is to compute a closest σ-extension within a distance-based setting, either by repairing S into a σ-extension of the AF, or by adjusting S to be a σ-extension containing (or not containing) a given argument. For each of the problems, we consider both iterative Boolean satisfiability (SAT) based approaches as well as directly solving the problems via Boolean optimization using maximum satisfiability (MaxSAT) solvers. We present results from an extensive empirical evaluation under several AF semantics σ using the ICCMA 2017 competition instances and several state-of-the-art solvers. The results indicate that the choice of the approach can play a significant role in the ability to solve these problems, and that a specific MaxSAT approach yields quite generally good results. Furthermore, with impact on SAT-based AF reasoning systems more generally, we demonstrate that, especially on dense AFs, taking into account the local structure of AFs can have a significant positive effect on the overall solving efficiency.