Song Y (2017)
Publication Language: English
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2017
Publisher: SCIENCE PRESS
Book Volume: 60
Pages Range: 361-378
Journal Issue: 2
DOI: 10.1007/s11425-015-0522-3
We propose an alternating direction method of multipliers (ADMM) for solving the state constrained optimization problems governed by elliptic equations. The unconstrained as well as box-constrained cases of the Dirichlet boundary control, Robin boundary control, and right-hand side control problems are considered here. These continuous optimization problems are transformed into discrete optimization problems by the finite element method discretization, then are solved by ADMM. The ADMM is an efficient first order algorithm with global convergence, which combines the decomposability of dual ascent with the superior convergence properties of the method of multipliers. We shall present exhaustive convergence analysis of ADMM for these different type optimization problems. The numerical experiments are performed to verify the efficiency of the method.
APA:
Song, Y. (2017). An alternating direction method of multipliers for elliptic equation constrained optimization problem. Science China-Mathematics, 60(2), 361-378. https://dx.doi.org/10.1007/s11425-015-0522-3
MLA:
Song, Yongcun. "An alternating direction method of multipliers for elliptic equation constrained optimization problem." Science China-Mathematics 60.2 (2017): 361-378.
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