An alternating direction method of multipliers for elliptic equation constrained optimization problem

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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)361-378
Journal / PublicationScience China Mathematics
Volume60
Issue number2
Publication statusPublished - 1 Feb 2017
Externally publishedYes

Abstract

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. © 2016, Science China Press and Springer-Verlag Berlin Heidelberg.

Research Area(s)

  • ADMM, elliptic equation constrained, optimal control problems

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