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ADMM for monotone operators: convergence analysis and rates

Banff International Research Station for Mathematical Innovation and Discovery

We propose a unifying scheme for several algorithms from the literature dedicated to the solving of monotone inclusion problems involving compositions with linear continuous operators in infinite dimensional Hilbert spaces. We show that a number of primal-dual algorithms for monotone inclusions and also the classical ADMM numerical scheme for convex optimization problems, along with some of its variants, can be embedded in this unifying scheme. While in the first part of the talk convergence results for the iterates are reported, the second part is devoted to the derivation of convergence rates obtained by combining variable metric techniques with strategies based on a suitable choice of dynamical step sizes. The talk is based on a joint work with Radu Bot.

Mathematics; Operations research, mathematical programming; Operator theory; Control/optimization/operation research

video/mp4

Author affiliation: Vienna

2018-03-24

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/64909

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/