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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.17450 |
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| _version_ | 1866929585316167680 |
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| author | Nam, Nguyen Mau Sharkansky, Jacob |
| author_facet | Nam, Nguyen Mau Sharkansky, Jacob |
| contents | In this paper, we explore the concept of $σ$-quasiconvexity for functions defined on normed vector spaces. This notion encompasses two important and well-established concepts: quasiconvexity and strong quasiconvexity. We start by analyzing certain operations on functions that preserve $σ$-quasiconvexity. Next, we present new results concerning the strong quasiconvexity of norm and Minkowski functions in infinite dimensions. Furthermore, we extend a recent result by F. Lara [16] on the supercoercive properties of strongly quasiconvex functions, with applications to the existence and uniqueness of minima, from finite dimensions to infinite dimensions. Finally, we address counterexamples related to strong quasiconvexity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17450 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Strong Quasiconvexity of Functions in Infinite Dimensions Nam, Nguyen Mau Sharkansky, Jacob Optimization and Control In this paper, we explore the concept of $σ$-quasiconvexity for functions defined on normed vector spaces. This notion encompasses two important and well-established concepts: quasiconvexity and strong quasiconvexity. We start by analyzing certain operations on functions that preserve $σ$-quasiconvexity. Next, we present new results concerning the strong quasiconvexity of norm and Minkowski functions in infinite dimensions. Furthermore, we extend a recent result by F. Lara [16] on the supercoercive properties of strongly quasiconvex functions, with applications to the existence and uniqueness of minima, from finite dimensions to infinite dimensions. Finally, we address counterexamples related to strong quasiconvexity. |
| title | On Strong Quasiconvexity of Functions in Infinite Dimensions |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2409.17450 |