Compact R-Continuity with Applications to Solving Inclusions and Convergence of Algorithms
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916933057642496 |
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| author | Le, Ba Khiet Mordukhovich, Boris S. Thera, Michel A. |
| author_facet | Le, Ba Khiet Mordukhovich, Boris S. Thera, Michel A. |
| contents | This paper investigates the notion of compact R-continuity and its specifications for set-valued mappings between Banach spaces. We reveal several important properties of compact R-continuity in general settings and show that in finite dimensions, this notion is supported by the classical Lojasiewicz inequality for analytic functions. An application of compact R-continuity and the obtained results is given to convergence analysis for a broad class of descent algorithms in nonsmooth optimization. We also show that this notion is instrumental for the design and justification of a novel R-class of algorithms to solve inclusion problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01872 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Compact R-Continuity with Applications to Solving Inclusions and Convergence of Algorithms Le, Ba Khiet Mordukhovich, Boris S. Thera, Michel A. Optimization and Control This paper investigates the notion of compact R-continuity and its specifications for set-valued mappings between Banach spaces. We reveal several important properties of compact R-continuity in general settings and show that in finite dimensions, this notion is supported by the classical Lojasiewicz inequality for analytic functions. An application of compact R-continuity and the obtained results is given to convergence analysis for a broad class of descent algorithms in nonsmooth optimization. We also show that this notion is instrumental for the design and justification of a novel R-class of algorithms to solve inclusion problems. |
| title | Compact R-Continuity with Applications to Solving Inclusions and Convergence of Algorithms |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2509.01872 |