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Invexity of supremum and infimum functions
Under suitable assumptions we establish the formulas for calculating generalised gradients and generalised directional derivatives in the Clarke sense of the supremum and the infimum of an infinite family of Lipschitz functions. From these results we derive the results ensuring such a supremum or in...
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| Published in: | Bulletin of the Australian Mathematical Society 2002-04, Vol.65 (2), p.289-306 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c396t-cd0537471e186cabb461246c41f70d2e583b97bc2d91a165ec06b3d0fa6e5d073 |
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| cites | cdi_FETCH-LOGICAL-c396t-cd0537471e186cabb461246c41f70d2e583b97bc2d91a165ec06b3d0fa6e5d073 |
| container_end_page | 306 |
| container_issue | 2 |
| container_start_page | 289 |
| container_title | Bulletin of the Australian Mathematical Society |
| container_volume | 65 |
| creator | Ha, Nguyen Xuan Van Luu, Do |
| description | Under suitable assumptions we establish the formulas for calculating generalised gradients and generalised directional derivatives in the Clarke sense of the supremum and the infimum of an infinite family of Lipschitz functions. From these results we derive the results ensuring such a supremum or infimum are an invex function when all functions of the invex. Applying these results to a class of mathematical programs, we obtain necessary and sufficient conditions for optimality. |
| doi_str_mv | 10.1017/S0004972700020335 |
| format | article |
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| fulltext | fulltext |
| identifier | ISSN: 0004-9727 |
| ispartof | Bulletin of the Australian Mathematical Society, 2002-04, Vol.65 (2), p.289-306 |
| issn | 0004-9727 1755-1633 |
| language | eng |
| recordid | cdi_proquest_journals_2786765680 |
| source | KB+ Cambridge University Press: JISC Collections:Full Collection Digital Archives (STM and HSS) |
| subjects | Infimum Mathematical analysis Mathematical programming |
| title | Invexity of supremum and infimum functions |
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