A parameterized Douglas–Rachford algorithm

Dongying Wang () and Xianfu Wang ()
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Dongying Wang: University of British Columbia
Xianfu Wang: University of British Columbia

Computational Optimization and Applications, 2019, vol. 73, issue 3, No 5, 839-869

Abstract: Abstract Based on a reparametrization of the Douglas–Rachford algorithm, we provide a principle of finding the least norm solution for a sum of two maximally monotone operators. The algorithm allows us to find the least norm solution to a sum of monotone operators, and even generally to find the least norm primal-dual solution to inclusions with mixtures of composite monotone operators. Three numerical results illustrate our results.

Keywords: Averaged mapping; Attouch–Thera type duality; Convex function; Firmly nonexpansive mapping; Kuhn–Tucker inclusion; Maximally monotone inclusion; Parameterized Douglas–Rachford splitting; Projection mapping; Proximal mapping; Resolvent; Primary 47H05; Secondary 65K05; 90C25 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10589-019-00088-8

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