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Chuyên mục:
Khoa học Tự nhiên (Tiếng Anh)
Ngày xuất bản:
27/04/2026
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Trích dẫn bài báo
Nguyen, L. T., Phan, T. D. M., & Pham, H. Q. (2026). Interval valued optimization problem on Hadarmard manifold: Wofle duality. Tạp chí Khoa học Đại học Đồng Tháp, 15(5), 41-50. https://doi.org/10.52714/dthu.ns.2145.1832
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Interval valued optimization problem on Hadarmard manifold: Wofle duality
Nội dung chính của bài viết
Tóm tắt
This paper will study about the duality for interval valued optimization problems on Hadamard manifolds. That is Wolfe dual problem with weak duality and strong duality. These results are the complement for the solvability of interval valued optimization problems on Hadamard manifolds.
Từ khóa
Hàm giá trị khoảng, Đối ngẫu Wofle, Đa tạp Hadamard, -khả vi.
Chi tiết bài viết
Bài báo này được cấp phép theo Creative Commons Attribution-NonCommercial 4.0 International License.
Tài liệu tham khảo
Absil, P. A., R. Mahony, and Sepulchre, R.(2008). Optimization Algorithms on Matrix Manifolds, Princeton University Press, Princeton, New York. DOI: 10.1515/9781400830244
Aguirre-Cipe, I., Lopez, R., Mallea, E., and Vásquez, L.(2021). A study of interval optimization problems, Optimization Letters, 15(3), 859-877. DOI: 10.1007/s11590-019-01496-9
Bacak, M.(2014). Convex Analysis and Optimization in Hadamard Spaces, De Gruyter. DOI: 10.1515/9783110361629
Bhurjee, A. and Panda, G.(2013). Efficient solution of interval optimization problem, Mathematical Method of Operations Research, 76(3), 273-288. DOI: 10.1007/s00186-012-0399-0
Diamond. P. and Kloeden P.E.(1994). Metric spaces of Fuzzy sets: theory and applications. Singapore:
World Scientific. DOI:10.1142/2326
Do Carmo, M.P.(1992). Riemannian Geometry, Birkhauser Boston.
Ghosh, D.(2017). Newton method to obtain efficient solutions of the optimization problems with interval-valued objective functions, Journal of Applied Mathematics and Computing, 53(1-2), 709-731. DOI: 10.1007/s12190-016-0990-2
Ghosh, D., Chauhan, R., Mesiar, R. and Debnath, A.(2020). Generalized Hukuhara Gâteaux and Fréchet derivatives of interval-valued functions and their application in optimization with interval-valued functions, Information Sciences, 510(4), 317-340. DOI: 10.1016/j.ins.2019.09.023
Ishibuchi H. and Tanaka H.(1990). Multiobjective programming in optimization of the interval
objective function, European Journal of Operational Research, 48(2):219–225. DOI: 10.1016/0377-2217(90)90375-L
Jana M. and Panda G.(2014). Solution of nonlinear interval vector optimization problem. Operational Research ,14:71–85. DOI: 10.1007/s12351-013-0137-2
Jost, J.(2011). Riemannian Geometry and Geometric Analysis, Universitext Book Series, Springer, Berlin Heidelberg.
Nguyen, L.T., Chang, Y.L., Hu, C.C., and Chen, J.S.(2023). Interval Optimization Problems on Hadamard manifolds, Journal of Nonlinear and Convex Analysis, 24(11), 2489-2511.
Nguyen, L.T., Chang, Y.L., Hu, C.C., and Chen, J.S.(2024). Optimality and KKT conditions for interval valued optimization problems on Hadamard manifolds, Optimization, DOI: 10.1080/02331934.2024.2375424.
Stefanini, L.(2008). Generalized Hukuhara differentiability of interval-valued functions and interval differential equations, Nonlinear Analysis, 71(3-4), 1311-1328. DOI: 10.1016/j.na.2008.12.005
Aguirre-Cipe, I., Lopez, R., Mallea, E., and Vásquez, L.(2021). A study of interval optimization problems, Optimization Letters, 15(3), 859-877. DOI: 10.1007/s11590-019-01496-9
Bacak, M.(2014). Convex Analysis and Optimization in Hadamard Spaces, De Gruyter. DOI: 10.1515/9783110361629
Bhurjee, A. and Panda, G.(2013). Efficient solution of interval optimization problem, Mathematical Method of Operations Research, 76(3), 273-288. DOI: 10.1007/s00186-012-0399-0
Diamond. P. and Kloeden P.E.(1994). Metric spaces of Fuzzy sets: theory and applications. Singapore:
World Scientific. DOI:10.1142/2326
Do Carmo, M.P.(1992). Riemannian Geometry, Birkhauser Boston.
Ghosh, D.(2017). Newton method to obtain efficient solutions of the optimization problems with interval-valued objective functions, Journal of Applied Mathematics and Computing, 53(1-2), 709-731. DOI: 10.1007/s12190-016-0990-2
Ghosh, D., Chauhan, R., Mesiar, R. and Debnath, A.(2020). Generalized Hukuhara Gâteaux and Fréchet derivatives of interval-valued functions and their application in optimization with interval-valued functions, Information Sciences, 510(4), 317-340. DOI: 10.1016/j.ins.2019.09.023
Ishibuchi H. and Tanaka H.(1990). Multiobjective programming in optimization of the interval
objective function, European Journal of Operational Research, 48(2):219–225. DOI: 10.1016/0377-2217(90)90375-L
Jana M. and Panda G.(2014). Solution of nonlinear interval vector optimization problem. Operational Research ,14:71–85. DOI: 10.1007/s12351-013-0137-2
Jost, J.(2011). Riemannian Geometry and Geometric Analysis, Universitext Book Series, Springer, Berlin Heidelberg.
Nguyen, L.T., Chang, Y.L., Hu, C.C., and Chen, J.S.(2023). Interval Optimization Problems on Hadamard manifolds, Journal of Nonlinear and Convex Analysis, 24(11), 2489-2511.
Nguyen, L.T., Chang, Y.L., Hu, C.C., and Chen, J.S.(2024). Optimality and KKT conditions for interval valued optimization problems on Hadamard manifolds, Optimization, DOI: 10.1080/02331934.2024.2375424.
Stefanini, L.(2008). Generalized Hukuhara differentiability of interval-valued functions and interval differential equations, Nonlinear Analysis, 71(3-4), 1311-1328. DOI: 10.1016/j.na.2008.12.005