New Douglas-Rachford algorithmic structures and their convergence analyses
Abstract: In this paper we study new algorithmic structures with Douglas- Rachford (DR) operators to solve convex feasibility problems. We propose to embed the basic two-set-DR algorithmic operator into the String-Averaging Projections (SAP) and into the Block-Iterative Pro- jection (BIP) algorithmic structures, thereby creating new DR algo- rithmic schemes that include the recently proposed cyclic Douglas- Rachford algorithm and the averaged DR algorithm as special cases. We further propose and investigate a new multiple-set-DR algorithmic operator. Convergence of all these algorithmic schemes is studied by using properties of strongly quasi-nonexpansive operators and firmly nonexpansive operators.
Keywords: Douglas-Rachford operator, string-averaging, block-iterative.
Category 1: Convex and Nonsmooth Optimization (Convex Optimization )
Citation: SIAM Journal on Optimization, accepted for publication.
Entry Submitted: 12/01/2015
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