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Second-order optimality conditions for locally Lipschitz vector optimization problems.
- Source :
-
Optimization . May2024, Vol. 73 Issue 5, p1551-1570. 20p. - Publication Year :
- 2024
-
Abstract
- In this paper, we derive primal and dual second-order necessary and sufficient optimality conditions for a vector optimization problem with equality and inequality constraints where the functions involved are locally Lipschitz. We introduce a weaker notion of second-order Abadie constraint qualification to derive second-order necessary conditions for weak local Pareto minima and strict local Pareto minima of order two in terms of Páles and Zeidan's second-order upper directional derivatives. Dual necessary conditions are derived for both types of minimal solutions in finite-dimensional spaces assuming the functions to be first-order continuously Fréchet differentiable. In the same setting, we derive dual and primal second-order sufficient optimality conditions for strict local Pareto minima of order two in terms of second-order lower directional derivatives. [ABSTRACT FROM AUTHOR]
- Subjects :
- *DIRECTIONAL derivatives
*FUNCTION spaces
Subjects
Details
- Language :
- English
- ISSN :
- 02331934
- Volume :
- 73
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 176582649
- Full Text :
- https://doi.org/10.1080/02331934.2023.2169046