Federated learning (FL) for medical image segmentation becomes more challenging in multi-task settings where clients might have different categories of labels represented in their data. For example, one client might have patient data with healthy pancreases only while datasets from other clients may contain cases with pancreatic tumors. The vanilla federated averaging algorithm makes it possible to obtain more generalizable deep learning-based segmentation models representing the training data from multiple institutions without centralizing datasets. However, it might be sub-optimal for the aforementioned multi-task scenarios. In this paper, we investigate heterogeneous optimization methods that show improvements for the automated segmentation of pancreas and pancreatic tumors in abdominal CT images with FL settings.