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Optimization techniques have been used for many years in the formulation and solution of computational problems arising in speech and language processing. Such techniques are found in the Baum-Welch, extended Baum-Welch (EBW), Rprop, and GIS algorithms, for example. Additionally, the use of regularization terms has been seen in other applications of sparse optimization. This paper outlines a range of problems in which optimization formulations and algorithms play a role, giving some additional details on certain application problems in machine translation, speaker/language recognition, and automatic speech recognition. Several approaches developed in the speech and language processing communities are described in a way that makes them more recognizable as optimization procedures. Our survey is not exhaustive and is complemented by other papers in this volume.