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论文类型：期刊论文
发表时间：2008-06-01
发表刊物：ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH
收录刊物：SCIE、EI
卷号：25
期号：3
页面范围：327-371
ISSN号：0217-5959
关键字：nonconvex optimization; nonlinear Lagrangian; dual algorithm; condition number; dual function
摘要：This paper establishes a theory framework of a class of nonlinear Lagrangians for solving nonlinear programming problems with inequality constraints. A set of conditions are proposed to guarantee the convergence of nonlinear Lagrangian algorithms, to analyze condition numbers of nonlinear Lagrangian Hessians as well as to develop the dual approaches. These conditions are satisfied by well-known nonlinear Lagrangians appearing in literature. The convergence theorem shows that the dual algorithm based on any nonlinear Lagrangian in the class is locally convergent when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions and the error bound solution, depending on the penalty parameter, is also established. The paper also develops the dual problems based on the proposed nonlinear Lagrangians, and the related duality theorem and saddle point theorem are demonstrated. Furthermore, it is shown that the condition numbers of Lagrangian Hessians at optimal solutions are proportional to the controlling penalty parameters. We report some numerical results obtained by using nonlinear Lagrangians.