Abstract
In this paper, primal and dual necessary/sufficient optimality conditions are investigated for vector optimization problem with set, cone and equality constraints. We establish some necessary optimality conditions for strict local Pareto minima in terms of contingent derivatives, contingent epiderivatives and contingent hypoderivatives with steady functions in Banach spaces to such problem. Under suitable assumptions, necessary optimality conditions become sufficient optimality conditions. Examples illustrate the applicability of the obtained results.
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The authors would like to express many thanks to two anonymous referees for careful reading of the manuscript, which improved the paper in its present form. Addionally, the authors are grateful to the editors for sending our manuscript to reviewers.
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Van Su, T., Hang, D.D. Optimality conditions in terms of contingent epiderivatives for strict local Pareto minima in vector optimization problems with constraints. Positivity 25, 1737–1760 (2021). https://doi.org/10.1007/s11117-021-00842-5
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DOI: https://doi.org/10.1007/s11117-021-00842-5
Keywords
- Vector optimization problem with constraints
- Optimality conditions
- Strict local Pareto minima
- Contingent epiderivatives
- Stable functions