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Glaucoma is a serious eye disease that can cause permanent blindness and is difficult to diagnose early. Optic disc (OD) and optic cup (OC) play a pivotal role in the screening of glaucoma. Therefore, accurate segmentation of OD and OC from fundus images is a key task in the automatic screening of glaucoma. In this paper, we designed a U-shaped convolutional neural network with multi-scale input and multi-kernel modules (MSMKU) for OD and OC segmentation. Such a design gives MSMKU a rich receptive field and is able to effectively represent multi-scale features. In addition, we designed a mixed maximum loss minimization learning strategy (MMLM) for training the proposed MSMKU. This training strategy can adaptively sort the samples by the loss function and re-weight the samples through data enhancement, thereby synchronously improving the prediction performance of all samples. Experiments show that the proposed method has obtained a state-of-the-art breakthrough result for OD and OC segmentation on the RIM-ONE-V3 and DRISHTI-GS datasets. At the same time, the proposed method achieved satisfactory glaucoma screening performance on the RIM-ONE-V3 and DRISHTI-GS datasets. On datasets with an imbalanced distribution between typical and rare sample images, the proposed method obtained a higher accuracy than existing deep learning methods.