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论文类型：期刊论文
发表时间：2015-08-01
发表刊物：JOURNAL OF GLOBAL OPTIMIZATION
收录刊物：SCIE、EI、Scopus
卷号：62
期号：4,SI
页面范围：675-694
ISSN号：0925-5001
关键字：Nonsmooth optimization; Constrained optimization; Smoothing function; Augmented Lagrangian method; Constraint qualification; Bilevel program
摘要：In this paper, we propose a smoothing augmented Lagrangian method for finding a stationary point of a nonsmooth and nonconvex optimization problem. We show that any accumulation point of the iteration sequence generated by the algorithm is a stationary point provided that the penalty parameters are bounded. Furthermore, we show that a weak version of the generalized Mangasarian Fromovitz constraint qualification (GMFCQ) at the accumulation point is a sufficient condition for the boundedness of the penalty parameters. Since the weak GMFCQ may be strictly weaker than the GMFCQ, our algorithm is applicable for an optimization problem for which the GMFCQ does not hold. Numerical experiments show that the algorithm is efficient for finding stationary points of general nonsmooth and nonconvex optimization problems, including the bilevel program which will never satisfy the GMFCQ.