Global convergence of modified augmented Lagrangian methods for nonlinear semidefinite programming
Global convergence of modified augmented Lagrangian methods for nonlinear semidefinite programming
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DOI：
10.1007/s10589-013-9568-1
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发表时间：
2013-05
影响因子：
2.2
通讯作者：
Huixian Wu;Hezhi Luo;Xiaodong Ding;Guanting Chen
中科院分区：
文献类型：
--
作者：
Huixian Wu;Hezhi Luo;Xiaodong Ding;Guanting Chen
本文研究了非线性半定规划的增广拉格朗日方法的全局收敛性。基于不同的算法策略，提出了求解NLSDP问题的四种改进增广拉格朗日方法。对所提方法的可能不可行的极限点进行了表征。证明了满足Mangasarian-Fromovitz约束条件的可行极限点是NLSDP的KKT点，而不需要乘子的有界性条件。初步的数值结果比较了改进的增广拉格朗日方法的性能。
We investigate in this paper global convergence properties of the augmented Lagrangian method for nonlinear semidefinite programming (NLSDP). Four modified augmented Lagrangian methods for solving NLSDP based on different algorithmic strategies are proposed. Possibly infeasible limit points of the proposed methods are characterized. It is proved that feasible limit points that satisfy the Mangasarian-Fromovitz constraint qualification are KKT points of NLSDP without requiring the boundedness condition of the multipliers. Preliminary numerical results are reported to compare the performance of the modified augmented Lagrangian methods.