Dialogue Discourse Parsing aims to identify the discourse links and relations between utterances, which has attracted more interest in recent years. Previous studies either adopt local optimization to independently select one parent for each utterance or use global optimization to directly get the tree representing the dialogue structure. However, the influence of these two optimization methods remains less explored. In this paper, we aim to systematically inspect their performance. Specifically, for local optimization, we use local loss during the training stage and a greedy strategy during the inference stage. For global optimization, We implement optimization of unlabeled and labeled trees by structured losses including Max-Margin and TreeCRF, and exploit Chu-Liu-Edmonds algorithm during the inference stage. Experiments shows that the performance of these two optimization methods is closely related to the characteristics of the dataset, and global optimization can reduce the burden of identifying long-range dependency relations.