Alternating direction method of multipliers for linear inverse problems

Yuling Jiao, Qinian Jin, Xiliang Lu, Weijie Wang

    Research output: Contribution to journalArticlepeer-review

    35 Citations (Scopus)

    Abstract

    In this paper we propose an iterative method using alternating direction method of multipliers (ADMM) strategy to solve linear inverse problems in Hilbert spaces with a general convex penalty term. When the data is given exactly, we give a convergence analysis of our ADMM algorithm without assuming the existence of a Lagrange multiplier. In case the data contains noise, we show that our method is a regularization method as long as it is terminated by a suitable stopping rule. Various numerical simulations are performed to test the efficiency of the method.

    Original languageEnglish
    Pages (from-to)2114-2137
    Number of pages24
    JournalSIAM Journal on Numerical Analysis
    Volume54
    Issue number4
    DOIs
    Publication statusPublished - 2016

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