Open Access
Issue |
RAIRO-Oper. Res.
Volume 58, Number 4, July-August 2024
|
|
---|---|---|
Page(s) | 3049 - 3067 | |
DOI | https://doi.org/10.1051/ro/2024118 | |
Published online | 01 August 2024 |
- N.L.H. Anh, Higher-order optimality conditions in set-valued optimization using Studniarski derivatives and applications to duality. Positivity 18 (2014) 449–473. [Google Scholar]
- N.L.H. Anh, Mixed type duality for set-valued optimization problems via higher-order radial epiderivatives. Numer. Func. Anal. Opt. 37 (2016) 823–838. [CrossRef] [Google Scholar]
- N.L.H. Anh, Sensitivity analysis in constrained set-valued optimization via Studniarski derivatives. Positivity 21 (2017) 255–272. [CrossRef] [MathSciNet] [Google Scholar]
- N.L.H. Anh and P.Q. Khanh, Higher-order optimality conditions in set-valued optimization using radial sets and radial derivatives. J Global Optim. 56 (2013) 519–536. [CrossRef] [MathSciNet] [Google Scholar]
- N.L.H. Anh, P.Q. Khanh and L.T. Tung, Higher-order radial derivatives and optimality conditions in nonsmooth vector optimization. Nonlinear Anal. Theor. 74 (2011) 7365–7379. [CrossRef] [Google Scholar]
- C.R. Chen, S.J. Li and K.L. Teo, Higher order weak epiderivatives and applications to duality and optimality conditions. Comput. Math. Appl. 57 (2009) 1389–1399. [Google Scholar]
- H.T.H. Diem, P.Q. Khanh and L.T. Tung, On higher-order sensitivity analysis in nonsmooth vector optimization. J. Optim. Theory Appl. 162 (2014) 463–488. [Google Scholar]
- F. Flores-Bazán and B. Jiménez, Strict efficiency in set-valued optimization. SIAM J. Control Optim. 48 (2009) 881–908. [CrossRef] [MathSciNet] [Google Scholar]
- W.Y. Han and G.L. Yu, Ekeland’s variational principle with a scalarization type weighted set order relation. J. Nonlinear Var. Anal. 7 (2023) 381–396. [Google Scholar]
- A.A. Khan, C. Tammer and C. Zălinescu, Set-valued optimization. Springer-Verlag, Berlin An (2016). [Google Scholar]
- S.J. Li and C.R. Chen, Higher order optimality conditions for Henig efficient solutions in set-valued optimization. J. Math. Anal. Appl. 323 (2006) 1184–1200. [CrossRef] [MathSciNet] [Google Scholar]
- D.T. Luc, Theory of Vector Optimization. Springer, Berlin (1989). [Google Scholar]
- Z.H. Peng and Y.H. Xu, New second-order tangent epiderivatives and applications to set-valued optimization. J. Optim. Theory Appl. 172 (2017) 128–140. [Google Scholar]
- Z.H. Peng, Z.P. Wan and Y.J. Guo, New higher-order weak lower inner epiderivatives and application to Karush-Kuhn-Tucker necessary optimality conditions in set-valued optimization. Jpn. J. Ind. Appl. Math. 37 (2020) 851–866. [CrossRef] [MathSciNet] [Google Scholar]
- T.H. Pham, Generalized higher-order semi-derivative of the perturbation maps in vector optimization. Jpn. J. Ind. Appl. Math. 40 (2023) 929–963. [CrossRef] [MathSciNet] [Google Scholar]
- T.V. Su and D.D. Hang, Second-order necessary and sufficient optimality conditions for constrained vector equilibrium problem with applications. Bull. Iran. Math Soc. 47 (2021) 1337–1362. [CrossRef] [Google Scholar]
- X.K. Sun and S.J. Li, Lower Studniarski derivative of the perturbation map in parametrized vector optimization. Optim. Lett. 5 (2011) 601–614. [CrossRef] [MathSciNet] [Google Scholar]
- A. Taa, Set-valued derivatives of multifunctions and optimality conditions. Numer. Funct. Anal. Optim. 19 (1998) 121–140. [Google Scholar]
- T. Tang, Q.L. Wang, X.Y. Zhang and Y.W. Zhai, Second-order weakly composed adjacent-generalized contingent epiderivatives and applications to composite set-valued optimization problems. Jpn. J. Ind. Appl. Math. 39 (2022) 319–350. [CrossRef] [MathSciNet] [Google Scholar]
- N.M. Tung and N.X.D. Bao, Higher-order set-valued Hadamard directional derivatives: calculus rules and sensitivity analysis of equilibrium problems and generalized equations. J. Global Optim. 83 (2022) 377–402. [CrossRef] [MathSciNet] [Google Scholar]
- Q.L. Wang and S.J. Li, Higher-order sensitivity analysis in nonconvexvector optimization. J. Ind. Manag. Optim. 6 (2010) 381–392. [CrossRef] [Google Scholar]
- Q.L. Wang and X.Y. Zhang, Second-order composed radial derivatives of the Benson proper perturbation map for parametric multi-objective optimization problems. Asia Pac. J. Oper. Res. 37 (2020) 2040011. [CrossRef] [MathSciNet] [Google Scholar]
- Y.H. Xu and Z.H. Peng, Higher-order sensitivity analysis in set-valued optimization under Henig efficiency. J. Ind. Manag. Optim. 13 (2017) 313–327. [CrossRef] [MathSciNet] [Google Scholar]
- X.M. Yang, D. Li and S.Y. Wang, Near-subconvexlikeness in vector optimization with set-valued functions. J. Optim. Theory Appl. 110 (2001) 413–427. [CrossRef] [MathSciNet] [Google Scholar]
- G.L. Yu, Optimality conditions in set optimization employing higher-order radial derivatives. Appl. Math. J. Chinese Univ. 32 (2017) 225–236. [CrossRef] [MathSciNet] [Google Scholar]
- Y.W. Zhai, Q.L. Wang, T. Tang and M. Lv, Optimality conditions for robust weakly efficient solutions in uncertain optimization. Optim. Lett. (2024) 1–25. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.