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We propose novel approaches for optimizing the detection performance in spoken language recognition. Two objective functions are designed to directly relate model parameters to two performance metrics of interest, the detection cost function and the area under the detection-error-tradeoff curve, respectively. Both metrics are approximated with differentiable functions of model parameters by using a smoothing function based on a class misclassification measure. The model parameters are optimized by using the generalized probabilistic descent algorithm. We conduct experiments on the NIST 2003 and 2005 Language Recognition Evaluation corpora. Results show that the proposed approaches effectively improve the performance over the maximum likelihood training approach.