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论文类型：期刊论文

发表时间：2018-08-01

发表刊物：NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS

收录刊物：SCIE、CPCI-S

卷号：25

期号：4,SI

ISSN号：1070-5325

关键字：finite-element method; inexact semiproximal ADMM; optimal control; semismooth Newton method

摘要：Elliptic optimal control problems with pointwise box constraints on the control are considered. To numerically solve elliptic optimal control problems with pointwise box constraints on the control, an inexact alternating direction method of multipliers (iADMM) is first proposed on the continuous level with the aim of solving discretized problems with moderate accuracy. Then, the standard piecewise linear finite element is employed to discretize the related subproblems appearing in each iteration of the iADMM algorithm. Such approach will give us the freedom to discretize two inner subproblems of the iADMM algorithm by different discretized scheme, respectively. More importantly, it should be emphasized that the discretized version of the iADMM algorithm can be regarded as a modification of the inexact semiproximal ADMM (isPADMM) algorithm. In order to obtain more accurate solution, the primal-dual active set method is used as a postprocessor of the isPADMM. Numerical results not only show that the isPADMM and the two-phase strategy are highly efficient but also show the mesh independence of the isPADMM.