Variable Metric ADMM for Solving Variational Inequalities with Monotone Operators over Affine Sets
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.
KeywordsADMM algorithm Primal-dual algorithm Monotone operators Convex optimization
AMS 2010 Subject Classification47H05 65K05 90C25
The first author has been partially supported by FWF (Austrian Science Fund), project I 2419-N32. The second author has been supported by FWF (Austrian Science Fund), project P 29809-N32. The third author has been partially supported by FWF (Austrian Science Fund), project I 2419-N32, and by the Doctoral Programme Vienna Graduate School on Computational Optimization (VGSCO), project W1260-N35.
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