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论文类型：期刊论文

发表时间：2014-06-03

发表刊物：OPTIMIZATION

收录刊物：SCIE

卷号：63

期号：6,SI

页面范围：899-920

ISSN号：0233-1934

关键字：semidefinite programming; nonlinear Lagrangian; augmented Lagrangian; dual algorithm; 90C22; 65K05

摘要：This paper focuses on the study of rescaling Lagrangians for solving nonconvex semidefinite programming problems. The rescaling nonlinear Lagrangians are generated by Lowner operators associated with convex real-valued functions. A set of conditions on the convex real-valued functions is proposed to guarantee the convergence of nonlinear rescaling Lagrangian algorithms. These conditions are satisfied by well-known nonlinear Lagrangians appeared in the literature. The convergence theorem shows that, under the second-order sufficient conditions with sigma-term and the strict constraint nondegeneracy condition, the nonlinear rescaling Lagrange algorithm is locally convergent when the penalty parameter is less than a threshold and the error bound of solution is proportional to the penalty parameter. Compared to the analysis in the nonlinear rescaling Lagrangian method for nonlinear programming, we have to deal with the sigma term in the convergence analysis.