Building on the achievements of the BiLSTM-CRF in named-entity recognition (NER), this paper introduces the BiLSTM-SSVM, an equivalent neural model where training is performed using a structured hinge loss. The typical loss functions used for evaluating NER are entity-level variants of the F1 score such as the CoNLL and MUC losses. Unfortunately, the common loss function used for training NER - the cross entropy - is only loosely related to the evaluation losses. For this reason, in this paper we propose a training approach for the BiLSTM-CRF that leverages a hinge loss bounding the CoNLL loss from above. In addition, we present a mixed hinge loss that bounds either the CoNLL loss or the Hamming loss based on the density of entity tokens in each sentence. The experimental results over four benchmark languages (English, German, Spanish and Dutch) show that training with the mixed hinge loss has led to small but consistent improvements over the cross entropy across all languages and four different evaluation measures.