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The performance of spoken language recognition system is typically formulated to reflect the detection cost and the strategic decision points along the detection-error-tradeoff curve. We propose a performance metrics optimization (PMO) approach to optimizing the detection performance of Gaussian mixture model classifiers. We design the objective functions to directly relate the model parameters to the performance metrics of interest, i.e., the detection cost function and the area under the detection-error-tradeoff curve. Both metrics are approximated by differentiable functions of model parameters. In this way, the model parameters can be optimized with the generalized probabilistic descent algorithm, a typical discriminative training technique. We conduct the experiments on the NIST 2003 and 2005 Language Recognition Evaluation corpora. The experimental results show that the PMO approach effectively improves the performance over the maximum-likelihood training approach.