Characterizations of Variational Convexity and Tilt Stability via Quadratic Bundles
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929665975779328 |
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| author | Khanh, Pham Duy Mordukhovich, Boris S. Phat, Vo Thanh Viet, Le Duc |
| author_facet | Khanh, Pham Duy Mordukhovich, Boris S. Phat, Vo Thanh Viet, Le Duc |
| contents | In this paper, we establish characterizations of variational $s$-convexity and tilt stability for prox-regular functions in the absence of subdifferential continuity via quadratic bundles, a kind of primal-dual generalized second-order derivatives recently introduced by Rockafellar. Deriving such characterizations in the effective pointbased form requires a certain revision of quadratic bundles investigated below. Our device is based on the notion of generalized twice differentiability and its novel characterization via classical twice differentiability of the associated Moreau envelopes combined with various limiting procedures for functions and sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04629 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterizations of Variational Convexity and Tilt Stability via Quadratic Bundles Khanh, Pham Duy Mordukhovich, Boris S. Phat, Vo Thanh Viet, Le Duc Optimization and Control 49J52, 49J53, 90C31 In this paper, we establish characterizations of variational $s$-convexity and tilt stability for prox-regular functions in the absence of subdifferential continuity via quadratic bundles, a kind of primal-dual generalized second-order derivatives recently introduced by Rockafellar. Deriving such characterizations in the effective pointbased form requires a certain revision of quadratic bundles investigated below. Our device is based on the notion of generalized twice differentiability and its novel characterization via classical twice differentiability of the associated Moreau envelopes combined with various limiting procedures for functions and sets. |
| title | Characterizations of Variational Convexity and Tilt Stability via Quadratic Bundles |
| topic | Optimization and Control 49J52, 49J53, 90C31 |
| url | https://arxiv.org/abs/2501.04629 |