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Support vector machines (SVMs) are theoretically well-justified machine learning techniques, which have also been successfully applied to many real-world domains. The use of optimization methodologies plays a central role in finding solutions of SVMs. This paper reviews representative and state-of-the-art techniques for optimizing the training of SVMs, especially SVMs for classification. The objective of this paper is to provide readers an overview of the basic elements and recent advances for training SVMs and enable them to develop and implement new optimization strategies for SVM-related research at their disposal.