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Several methods have been proposed to infer gene regulatory networks from time course gene expression data. As the number of genes is much larger than the number of time points at which gene expression (mRNA concentration) is measured, most existing methods need some ad hoc assumptions to infer a unique gene regulatory network from time course gene expression data. It is well known that gene regulatory networks are sparse and stable. However, inferred network from most existing methods may not be stable. In this paper we propose a method to infer sparse and stable gene regulatory networks from time course gene expression data. Instead of ad hoc assumption, we formulate the inference of sparse and stable gene regulatory networks as constraint optimization problems, which can be easily solved. To investigate the performance of our proposed method, computational experiments are conducted on synthetic datasets.