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摘要
In this paper, we focus on the minimization problem with , which is challenging due to the norm being non-Lipschizian. In theory, we derive computable lower bounds for nonzero entries of the generalized first-order stationary points of minimization, and hence of its local minimizers. In algorithms, based on three locally Lipschitz continuous -approximation to norm, we design several iterative reweighted and methods to solve those approximation problems. Furthermore, we show that any accumulation point of the sequence generated by these methods is a generalized first-order stationary point of minimization. This result, in particular, applies to the iterative reweighted methods based on the new Lipschitz continuous -approximation introduced by Lu (Math Program 147(1-2):277-307, 2014), provided that the approximation parameter is below a threshold value. Numerical results are also reported to demonstrate the efficiency of the proposed methods.
