Regularized Jacobi-type ADMM-methods for a class of separable convex optimization problems in Hilbert spaces

Eike Börgens () and Christian Kanzow ()
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Eike Börgens: University of Würzburg
Christian Kanzow: University of Würzburg

Computational Optimization and Applications, 2019, vol. 73, issue 3, No 2, 755-790

Abstract: Abstract We consider a regularized version of a Jacobi-type alternating direction method of multipliers (ADMM) for the solution of a class of separable convex optimization problems in a Hilbert space. The analysis shows that this method is equivalent to the standard proximal-point method applied in a Hilbert space with a transformed scalar product. The method therefore inherits the known convergence results from the proximal-point method and allows suitable modifications to get a strongly convergent variant. Some additional properties are also shown by exploiting the particular structure of the ADMM-type solution method. Applications and numerical results are provided for the domain decomposition method and potential (generalized) Nash equilibrium problems in a Hilbert space setting.

Keywords: Alternating direction method of multipliers; Hilbert space; Proximal-point method; Separable convex optimization; Global convergence (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10589-019-00087-9

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