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New Second-Order Optimality Conditions for Vector Equilibrium Problems with Constraints in Terms of Contingent Derivatives

New Second-Order Optimality Conditions for Vector Equilibrium Problems with Constraints in Terms... Abstract In this paper, we establish the primal and dual second-order necessary and sufficient optimality conditions for (local) weakly efficient solutions of vector equilibrium problems with constraints in terms of contingent derivatives with 2-steady functions in real finite spaces. Using the 2-steadiness of objective and constraint functions at a given optimal point, the second-order necessary conditions for weakly efficient solutions of constrained vector equilibrium problems are derived. Under the suitable assumptions on 2-steadiness of objective and constraint functions, the dual second-order necessary optimality conditions will become the dual second-order sufficient optimality conditions. We also give several examples that illustrate our results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Brazilian Mathematical Society, New Series Springer Journals

New Second-Order Optimality Conditions for Vector Equilibrium Problems with Constraints in Terms of Contingent Derivatives

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References (42)

Publisher
Springer Journals
Copyright
2019 Sociedade Brasileira de Matemática
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/s00574-019-00157-w
Publisher site
See Article on Publisher Site

Abstract

Abstract In this paper, we establish the primal and dual second-order necessary and sufficient optimality conditions for (local) weakly efficient solutions of vector equilibrium problems with constraints in terms of contingent derivatives with 2-steady functions in real finite spaces. Using the 2-steadiness of objective and constraint functions at a given optimal point, the second-order necessary conditions for weakly efficient solutions of constrained vector equilibrium problems are derived. Under the suitable assumptions on 2-steadiness of objective and constraint functions, the dual second-order necessary optimality conditions will become the dual second-order sufficient optimality conditions. We also give several examples that illustrate our results.

Journal

Bulletin of the Brazilian Mathematical Society, New SeriesSpringer Journals

Published: Jun 1, 2020

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