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Uniqueness of DRS as the 2 Operator Resolvent-Splitting and Impossibility of 3 Operator Resolvent-Splitting

Ernest K. Ryu(eryu***at***math.ucla.edu)

Abstract: Given the success of Douglas-Rachford splitting (DRS), it is natural to ask whether DRS can be generalized. Are there are other 2 operator splittings? Can DRS be generalized to 3 operators? This work presents the answers: no and no. In a certain sense, DRS is the unique 2 operator resolvent-splitting, and generalizing DRS to 3 operators is impossible without lifting, where lifting roughly corresponds to enlarging the problem size. The impossibility result further raises a question. How much lifting is necessary to generalize DRS to 3 operators? This work presents the answer by providing a novel 3 operator resolvent-splitting with provably minimal lifting that directly generalizes DRS.


Category 1: Convex and Nonsmooth Optimization (Convex Optimization )


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Entry Submitted: 02/21/2018
Entry Accepted: 02/21/2018
Entry Last Modified: 02/21/2018

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