In this talk, we examine some fundamental limitations of fixed point algorithms for finding a zero in the sum of n ≥ 2 maximally monotone operators using their resolvents. A common approach to this problem involves reformulating as an equivalent two operator inclusion within an n - fold Cartesian product space and applying the Douglas--Rachford algorithm. In the setting where each resolvent may only be evaluated once per iteration, we show that any fixed point algorithm is necessarily defined on a d - fold Cartesian product space with d ≥ n − 1. Further, we show this is unimprovable by providing a new family of methods which attain the lower bound. Applications in decentralised operator splitting will be discussed.
This talk is based on recent joint work with Yura Malitsky: arxiv.org/abs/2108.02897
Resolvent Splitting with Minimal Lifting
08.11.2021 15:30 - 16:30
Organiser:
R. I. Boț (U Wien), S. Sabach (Technion - Israel Institute of Technology Haifa), M. Staudigl (Maastricht U)
Location:
Zoom Meeting
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