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Finding best approximation pairs for two intersections of closed convex sets
- Source :
- Computational Optimization and Applications. 81:289-308
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
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.
- Subjects :
- 021103 operations research
Control and Optimization
Applied Mathematics
0211 other engineering and technologies
Regular polygon
010103 numerical & computational mathematics
02 engineering and technology
01 natural sciences
65K05 (Primary) 47H09, 90C25 (Secondary)
Computational Mathematics
Optimization and Control (math.OC)
FOS: Mathematics
0101 mathematics
Projection (set theory)
Mathematics - Optimization and Control
Algorithm
Mathematics
Subjects
Details
- ISSN :
- 15732894 and 09266003
- Volume :
- 81
- Database :
- OpenAIRE
- Journal :
- Computational Optimization and Applications
- Accession number :
- edsair.doi.dedup.....3a8eb465ee9af0779b18844366c58ee4