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论文类型：期刊论文
发表时间：2015-06-01
发表刊物：ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH
收录刊物：SCIE、EI、Scopus
卷号：32
期号：3
ISSN号：0217-5959
关键字：Nonlinear Lagrangian method; constrained optimization problems; penalty parameter; rate of convergence
摘要：It is well-known that the linear rate of convergence can be established for the classical augmented Lagrangian method for constrained optimization problems without strict complementarity. Whether this result is still valid for other nonlinear Lagrangian methods (NLM) is an interesting problem. This paper proposes a nonlinear Lagrangian function based on Fischer-Burmeister (F-B) nonlinear complimentarity problem (NCP) function for constrained optimization problems. The rate of convergence of this NLM is analyzed under the linear independent constraint qualification and the strong second order sufficient condition without strict complementarity when subproblems are assumed to be solved exactly and inexactly, respectively. Interestingly, it is demonstrated that the Lagrange multipliers associating with inactive inequality constraints at the local minimum point converge to zeros superlinearly. Several illustrative examples are reported to show the behavior of the NLM.