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In this paper, we propose class-discriminative kernel sparse representation-based classification (KSRC) using multi-objective optimization (MOO) called KSRC 2.0. In sparse representation-based classification (SRC), both dictionary and residuals (reconstruction errors) play an important role in classifying a sample. Thus, discriminative dictionary and residuals are required to achieve high classification performance. To generate discriminative dictionary and residuals from training data sets, we formulate multi-objective functions via the Fisher discrimination criterion that minimizes distances within and maximizes distances between classes. Then, we solve them by using MOO, which can optimize conflicting objectives at the same time, and obtain component importance factors to make dictionary and residuals class-discriminative. Extensive experiments on publicly available databases demonstrate that the proposed KSRC 2.0 enhances the class separability of KSRC and achieves high classification performance.