Variable Metric ADMM for Solving Variational Inequalities with Monotone Operators over Affine Sets

Radu Ioan Boţ (), Ernö Robert Csetnek () and Dennis Meier ()
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Radu Ioan Boţ: University of Vienna, Faculty of Mathematics
Ernö Robert Csetnek: University of Vienna, Faculty of Mathematics
Dennis Meier: University of Vienna, Faculty of Mathematics

Chapter Chapter 4 in Splitting Algorithms, Modern Operator Theory, and Applications, 2019, pp 91-112 from Springer

Abstract: Abstract We propose an iterative scheme for solving variational inequalities with monotone operators over affine sets in an infinite dimensional Hilbert space setting. We show that several primal-dual algorithms in the literature as well as the classical ADMM algorithm for convex optimization problems, together with some of its variants, are encompassed by the proposed numerical scheme. Furthermore, we carry out a convergence analysis of the generated iterates and provide convergence rates by using suitable dynamical step sizes together with variable metric techniques.

Keywords: ADMM algorithm; Primal-dual algorithm; Monotone operators; Convex optimization; 47H05; 65K05; 90C25 (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-25939-6_4

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DOI: 10.1007/978-3-030-25939-6_4

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