Inexact Proximal Point Method Using Quasi-Distances for Optimization of KL Functions
An inexact proximal point algorithm using quasi-distances is introduced to give a solution of a minimization problem in the Euclidean space. This algorithm has been motivated by the proximal method introduced by Attouch, Bolte and Svaiter [1] but in this case we consider quasi-distance instead of th...
| Authors: | , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2022 |
| Country: | Perú |
| Institution: | Universidad Nacional Mayor de San Marcos |
| Repository: | Revistas - Universidad Nacional Mayor de San Marcos |
| Language: | Spanish |
| OAI Identifier: | oai:revistasinvestigacion.unmsm.edu.pe:article/23144 |
| Online Access: | https://revistasinvestigacion.unmsm.edu.pe/index.php/matema/article/view/23144 |
| Access Level: | Open access |
| Keyword: | Kurdyka-Lojasiewicz inequality quasi-distances proximal point algo-rithm Desigualdad de Kurdyka-Lojasewicz cuasi-distancia algoritmo de punto proximal. |
| Summary: | An inexact proximal point algorithm using quasi-distances is introduced to give a solution of a minimization problem in the Euclidean space. This algorithm has been motivated by the proximal method introduced by Attouch, Bolte and Svaiter [1] but in this case we consider quasi-distance instead of the Euclidean distance, functions satisfying the Kurdyka-Lojasewicz inequality, vector errors in the critical point of the proximal subproblems. We obtain, under some additional assumptions, the global convergence of the sequence generated by the algorithm to a critical point of the problem. |
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