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

In: Splitting Algorithms, Modern Operator Theory, and Applications

Author

Listed:
  • 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)

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.

Suggested Citation

  • Radu Ioan Boţ & Ernö Robert Csetnek & Dennis Meier, 2019. "Variable Metric ADMM for Solving Variational Inequalities with Monotone Operators over Affine Sets," Springer Books, in: Heinz H. Bauschke & Regina S. Burachik & D. Russell Luke (ed.), Splitting Algorithms, Modern Operator Theory, and Applications, chapter 0, pages 91-112, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-25939-6_4
    DOI: 10.1007/978-3-030-25939-6_4
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