Finding best approximation pairs for two intersections of closed convex sets

Heinz H. Bauschke (), Shambhavi Singh () and Xianfu Wang ()
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Heinz H. Bauschke: University of British Columbia
Shambhavi Singh: University of British Columbia
Xianfu Wang: University of British Columbia

Computational Optimization and Applications, 2022, vol. 81, issue 1, No 10, 289-308

Abstract: Abstract The problem of finding a best approximation pair of two sets, which in turn generalizes the well known convex feasibility problem, has a long history that dates back to work by Cheney and Goldstein in 1959. In 2018, Aharoni, Censor, and Jiang revisited this problem and proposed an algorithm that can be used when the two sets are finite intersections of halfspaces. Motivated by their work, we present alternative algorithms that utilize projection and proximity operators. Our modeling framework is able to accommodate even convex sets. Numerical experiments indicate that these methods are competitive and sometimes superior to the one proposed by Aharoni et al.

Keywords: Aharoni–Censor–Jiang algorithm; Best approximation pair; Douglas–Rachford algorithm; Dual-based proximal method; Proximal distance algorithm; Stochastic subgradient descent; Primary 65K05; Secondary 47H09; 90C25 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10589-021-00324-0

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