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Understanding a social network is a fundamental problem in social network analysis because of its numerous applications. Recently, user engagement in networks has received extensive attention from many research groups. However, most user engagement models focus on global user engagement to maximize (or minimize) the number of engaged users. In this study, we formulate the so-called Local User Engagement Maximization (LUEM) problem. We prove that the LUEM problem is NP-hard. To obtain high-quality results, we propose an approximation algorithm that incorporates a traditional hill-climbing method. To improve efficiency, we propose an efficient pruning strategy while maintaining effectiveness. In addition, by observing the relationship between the degree and user engagement, we propose an efficient heuristic algorithm that preserves effectiveness. Finally, we conducted extensive experiments on ten real-world networks to demonstrate the superiority of the proposed algorithms. We observed that the proposed algorithm achieved up to 605% more engaged users compared to the best baseline algorithms.