Sparse multinomial logistic regression has recently received widespread attention. It provides a useful tool for solving multi-classification problems in various fields, such as signal and image processing, machine learning and disease diagnosis. In this paper, we first study the group sparse multinomial logistic regression model and establish its optimality conditions. Based on the theoretical results of this model, we hence propose an efficient algorithm called the subspace quadratic regularization algorithm to compute a stationary point of a given problem. This algorithm enjoys excellent convergence properties, including the global convergence and locally quadratic convergence. Finally, our numerical results on standard benchmark data clearly demonstrate the superior performance of our proposed algorithm in terms of logistic loss value, sparsity recovery and computational time.

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