Interval valued optimization problem on Hadarmard manifold: Wofle duality

Các tác giả

  • Le Tram Nguyen
  • Tran Duc Minh Phan
  • Huu Quyen Pham

DOI:

https://doi.org/10.52714/dthu.ns.2145.1832

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.

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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

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Đã Xuất bản

2026-04-27

Số

Chuyên mục

Khoa học Tự nhiên (Tiếng Anh)