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RESEARCH PRODUCT
Strengthened splitting methods for computing resolvents
Francisco J. Aragón ArtachoRubén CampoyMatthew K. Tamsubject
Splitting algorithmControl and Optimization0211 other engineering and technologies47H05 90C30 65K05Elliptic pdesMonotonic function02 engineering and technology01 natural sciencesMonotone operatorOperator (computer programming)Development (topology)Estadística e Investigación OperativaFOS: Mathematics0101 mathematicsImage denoisingResolventMathematics - Optimization and ControlMathematicsResolvent021103 operations researchApplied Mathematics010102 general mathematicsAlgebraComputational MathematicsMonotone polygonOptimization and Control (math.OC)StrengtheningKey (cryptography)description
In this work, we develop a systematic framework for computing the resolvent of the sum of two or more monotone operators which only activates each operator in the sum individually. The key tool in the development of this framework is the notion of the “strengthening” of a set-valued operator, which can be viewed as a type of regularisation that preserves computational tractability. After deriving a number of iterative schemes through this framework, we demonstrate their application to best approximation problems, image denoising and elliptic PDEs. FJAA and RC were partially supported by the Ministry of Science, Innovation and Universities of Spain and the European Regional Development Fund (ERDF) of the European Commission, Grant PGC2018-097960-B-C22. MKT is supported in part by ARC grant DE200100063.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-08-20 | Computational Optimization and Applications |