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Douglas-Rachford Splitting for Pathological Convex Optimization

Ernest K. Ryu(eryu***at***math.ucla.edu)
Yanli Liu(yanli***at***math.ucla.edu)
Wotao Yin(wotaoyin***at***math.ucla.edu)

Abstract: Despite the vast literature on DRS, there has been very little work analyzing their behavior under pathologies. Most analyses assume a primal solution exists, a dual solution exists, and strong duality holds. When these assumptions are not met, i.e., under pathologies, the theory often breaks down and the empirical performance may degrade significantly. In this paper, we establish that DRS only requires strong duality to work, in the sense that asymptotically iterates are approximately feasible and approximately optimal.

Keywords: Douglas-Rachford splitting, Inconsistent case, Strong duality, Nonexpansive mapping, Fixed point, Displacement vector, Improving direction, Primal subvalue.

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )


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Entry Submitted: 01/19/2018
Entry Accepted: 01/19/2018
Entry Last Modified: 01/19/2018

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