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Kou Caixia1; Chen Zhongwen2; Dai Yuhong3; Han Haifei4
Source Publicationjournalofcomputationalmathematics
AbstractAn augmented Lagrangian trust region method with a bi-object strategy is proposed for solving nonlinear equality constrained optimization, which falls in between penalty-type methods and penalty-free ones. At each iteration, a trial step is computed by minimizing a quadratic approximation model to the augmented Lagrangian function within a trust region. The model is a standard trust region subproblem for unconstrained optimization and hence can efficiently be solved by many existing methods. To choose the penalty parameter, an auxiliary trust region subproblem is introduced related to the constraint violation. It turns out that the penalty parameter need not be monotonically increasing and will not tend to infinity. A bi-object strategy, which is related to the objective function and the measure of constraint violation, is utilized to decide whether the trial step will be accepted or not. Global convergence of the method is established under mild assumptions. Numerical experiments are made, which illustrate the efficiency of the algorithm on various difficult situations.
Funding Project[Chinese NSF] ; [National 973 Program of China]
Document Type期刊论文
2.School of Mathematical Sciences,Soochow University
Recommended Citation
GB/T 7714
Kou Caixia,Chen Zhongwen,Dai Yuhong,et al. anaugmentedlagrangiantrustregionmethodwithabiobjectstrategy[J]. journalofcomputationalmathematics,2018,36(3):331.
APA Kou Caixia,Chen Zhongwen,Dai Yuhong,&Han Haifei.(2018).anaugmentedlagrangiantrustregionmethodwithabiobjectstrategy.journalofcomputationalmathematics,36(3),331.
MLA Kou Caixia,et al."anaugmentedlagrangiantrustregionmethodwithabiobjectstrategy".journalofcomputationalmathematics 36.3(2018):331.
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