The Elicited Progressive Decoupling Algorithm: A Note on the Rate of Convergence and a Preliminary Numerical Experiment on the Choice of Parameters
The paper studies the progressive decoupling algorithm (PDA) of Rockafellar and focuses on the elicited version of the algorithm. Based on a generalized Yosida-regularization of Spingarn’s partial inverse of an elicitable operator, it is shown that the elicited progressive decoupling algorithm (EPDA...
| Main Authors: | , |
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| Format: | Journal Article |
| Language: | English |
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SPRINGER
2021
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| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/91426 |
| _version_ | 1848765517305741312 |
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| author | Sun, Jie Zhang, M. |
| author_facet | Sun, Jie Zhang, M. |
| author_sort | Sun, Jie |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | The paper studies the progressive decoupling algorithm (PDA) of Rockafellar and focuses on the elicited version of the algorithm. Based on a generalized Yosida-regularization of Spingarn’s partial inverse of an elicitable operator, it is shown that the elicited progressive decoupling algorithm (EPDA), in a particular nonmonotone setting, linearly converges at a rate that could be viewed as the rate of a rescaled PDA, which may provide certain guidance to the selection of the parameters in computational practice. A preliminary numerical experiment shows that the choice of the elicitation constant has an impact on the efficiency of the EPDA. It is also observed that the influence of the elicitation constant is generally weaker than the proximal constant in the algorithm. |
| first_indexed | 2025-11-14T11:36:30Z |
| format | Journal Article |
| id | curtin-20.500.11937-91426 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T11:36:30Z |
| publishDate | 2021 |
| publisher | SPRINGER |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-914262023-05-03T07:42:01Z The Elicited Progressive Decoupling Algorithm: A Note on the Rate of Convergence and a Preliminary Numerical Experiment on the Choice of Parameters Sun, Jie Zhang, M. Science & Technology Physical Sciences Mathematics, Applied Mathematics Proximal point algorithm Progressive decoupling algorithm Stochastic variational inequality PROXIMAL POINT ALGORITHM MONOTONE OPERATORS The paper studies the progressive decoupling algorithm (PDA) of Rockafellar and focuses on the elicited version of the algorithm. Based on a generalized Yosida-regularization of Spingarn’s partial inverse of an elicitable operator, it is shown that the elicited progressive decoupling algorithm (EPDA), in a particular nonmonotone setting, linearly converges at a rate that could be viewed as the rate of a rescaled PDA, which may provide certain guidance to the selection of the parameters in computational practice. A preliminary numerical experiment shows that the choice of the elicitation constant has an impact on the efficiency of the EPDA. It is also observed that the influence of the elicitation constant is generally weaker than the proximal constant in the algorithm. 2021 Journal Article http://hdl.handle.net/20.500.11937/91426 10.1007/s11228-021-00613-0 English SPRINGER fulltext |
| spellingShingle | Science & Technology Physical Sciences Mathematics, Applied Mathematics Proximal point algorithm Progressive decoupling algorithm Stochastic variational inequality PROXIMAL POINT ALGORITHM MONOTONE OPERATORS Sun, Jie Zhang, M. The Elicited Progressive Decoupling Algorithm: A Note on the Rate of Convergence and a Preliminary Numerical Experiment on the Choice of Parameters |
| title | The Elicited Progressive Decoupling Algorithm: A Note on the Rate of Convergence and a Preliminary Numerical Experiment on the Choice of Parameters |
| title_full | The Elicited Progressive Decoupling Algorithm: A Note on the Rate of Convergence and a Preliminary Numerical Experiment on the Choice of Parameters |
| title_fullStr | The Elicited Progressive Decoupling Algorithm: A Note on the Rate of Convergence and a Preliminary Numerical Experiment on the Choice of Parameters |
| title_full_unstemmed | The Elicited Progressive Decoupling Algorithm: A Note on the Rate of Convergence and a Preliminary Numerical Experiment on the Choice of Parameters |
| title_short | The Elicited Progressive Decoupling Algorithm: A Note on the Rate of Convergence and a Preliminary Numerical Experiment on the Choice of Parameters |
| title_sort | elicited progressive decoupling algorithm: a note on the rate of convergence and a preliminary numerical experiment on the choice of parameters |
| topic | Science & Technology Physical Sciences Mathematics, Applied Mathematics Proximal point algorithm Progressive decoupling algorithm Stochastic variational inequality PROXIMAL POINT ALGORITHM MONOTONE OPERATORS |
| url | http://hdl.handle.net/20.500.11937/91426 |