张旭平

个人信息Personal Information

副教授

硕士生导师

性别:男

毕业院校:大连理工大学

学位:博士

所在单位:数学科学学院

学科:计算数学

办公地点:创新园大厦A1025

联系方式:0411-84708351-8025

电子邮箱:zhangxp@dlut.edu.cn

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A FE-ADMM ALGORITHM FOR LAVRENTIEV-REGULARIZED STATE-CONSTRAINED ELLIPTIC CONTROL PROBLEM

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论文类型:期刊论文

发表时间:2019-04-11

发表刊物:ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS

收录刊物:SCIE、EI

卷号:25

ISSN号:1292-8119

关键字:Optimal control; Pointwise state constraints; Lavrentiev regularization; Error estimates; Heterogeneous ADMM; Two-phase strategy

摘要:In this paper, Elliptic control problems with pointwise box constraints on the state is considered, where the corresponding Lagrange multipliers in general only represent regular Borel measure functions. To tackle this difficulty, the Lavrentiev regularization is employed to deal with the state constraints. To numerically discretize the resulted problem, full piecewise linear finite element discretization is employed. Estimation of the error produced by regularization and discretization is done. The error order of full discretization is not inferior to that of variational discretization because of the Lavrentiev-regularization. Taking the discretization error into account, algorithms of high precision do not make much sense. Utilizing efficient first-order algorithms to solve discretized problems to moderate accuracy is sufficient. Then a heterogeneous alternating direction method of multipliers (hADMM) is proposed. Different from the classical ADMM, our hADMM adopts two different weighted norms in two subproblems respectively. Additionally, to get more accurate solution, a two-phase strategy is presented, in which the primal-dual active set (PDAS) method is used as a postprocessor of the hADMM. Numerical results not only verify error estimates but also show the efficiency of the hADMM and the two-phase strategy.