Mở rộng nguyên lý biến phân Ekeland cho hàm có giá trị khoảng dựa trên tính nửa liên tục inner
,
,
,
và
*
Article Sidebar
Full Text: 
PDF
Abstract
In this paper, the inner semicontinuity and weakly boundedness from below of interval-valued functions were used to get a generalized Ekeland’s variational principle. Many example are provided to highlight relations of this results to existing ones, including their advantages
Tóm tắt
Trong bài báo này, tính nửa liên tục inner và tính bị chặn dưới yếu của hàm có giá trị khoảng được sử dụng để đưa ra phiên bản mở rộng của nguyên lý biến phân Ekeland. Nhiều ví dụ cụ thể được đưa ra để làm rõ mối quan hệ giữa kết quả này với các kết quả đã công bố trước đó, bao gồm phân tích các thuận lợi của chúng.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Tài liệu tham khảo
Ahmad, I., Jayswal, A., Al-Homidan, S., & Banerjee, J. (2019). Sufficiency and duality in intervalvalued variational programming. Neural Computing and Applications, 31, 4423–4433. https://doi.org/10.1007/s00521-017-3307-y
Aubin, J. P., & Ekeland, I. (1984). Applied Nonlinear Analysis. Wiley, NewYork.
Caristi, J. (1976). Fixed point theorem for mappings satisfying inwardness conditions. Transactions of the American Mathematical Society, 215, 241-251.
https://doi.org/10.1090/S0002-9947-1976-0394329-4
Chalco-Cano, Y., Rufían-Lizana, A., Román-Flores, H., & Jiménez-Gamero, M.D. (2013). Calculus for interval-valued functions using generalized Hukuhara derivative and applications. Fuzzy Sets and Systems, 219, 49–6. https://doi.org/10.1016/j.fss.2012.12.004
Daneš, J. (1972). A geometric theorem useful in nonlinear analysis. Bollettino dell'Unione Matematica Italiana, 6(4), 369-375.
Ekeland, I. (1974). On the variational principle. Journal of Mathematical Analysis and Applications, 47(3), 324-353. https://doi.org/10.1016/0022-247X(74)90025-0
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, 709–731. DOI:10.1007/s12190-016-0990-2
Ghosh, D., Bhuiya, S.K., & Patra, L.K. (2018). A saddle point characterization of efficient solutions for interval optimization problems. Journal of Applied Mathematics and Computing, 58, 193–217. DOI:10.1007/s12190-017-1140-1
Ghosh, D., Chauhan, R.S., Mesiar, R., & Debnath, A.K., (2020a). Generalized Hukuhara Gâteaux and Fréchet derivatives of interval-valued functions and their application in optimization with interval-valued functions. Information Sciences, 510, 317–340. https://doi.org/10.1016/j.ins.2019.09.023
Ghosh, D., Debnath, A.K., & Pedrycz, W. (2020b). A variable and a fixed ordering of intervals and their application in optimization with interval-valued functions. International Journal of Approximate Reasoning, 121, 187–205. https://doi.org/10.1016/j.ijar.2020.03.004
Ghosh, D., Singh, A., Shukla, K.K., & Manchanda, K. (2019). Extended Karush-Kuhn-Tucker condition for constrained interval optimization problems and its application in support vector machines. Information Sciences, 504, 276–292. https://doi.org/10.1016/j.ins.2019.07.017
Ishibuchi, H., & Tanaka, H. (1990). Multiobjective programming in optimization of the interval objective function. European Journal of Operational Research, 48, 219–225. https://doi.org/10.1016/0377-2217(90)90375-L
Penot, J. P. (1986). The drop theorem, the petal theorem and Ekeland’s variational principle. Nonlinear Analysis, 10(9), 813-822. https://doi.org/10.1016/0362-546X(86)90069-6
Phelps, R. R. (1974). Support cones in Banach spaces and their applications. Advances in Mathematics, 13, 1-19. https://doi.org/10.1016/0001-8708(74)90062-0
Moore, R.E., (1966). Interval Analysis. New Jersey, Englewood Cliffs, Prentice-Hall.
Rockafellar, R. T., & Wets, R.J.-B. (2009). Variational Analysis. Springer, Berlin.
Stefanini, L., & Bede, B. (2009). Generalized Hukuhara differentiability of interval-valued functions and interval differential equations. Nonlinear Analysis: Theory, Methods & Applications, 71, 1311–1328. https://doi.org/10.1016/j.na.2008.12.005
Singh, D., Dar, B.A., & Kim, D. (2016). KKT optimality conditions in interval valued multiobjective programming with generalized differentiable functions. European Journal of Operational Research, 254, 29–39. https://doi.org/10.1016/j.ejor.2016.03.042
Wu, H.C., (2007). The Karush-Kuhn-Tucker optimality conditions in an optimization problem with interval-valued objective function. European Journal of Operational Research, 176, 46–59.
https://doi.org/10.1016/j.ejor.2005.09.007
Wu, H.C., (2008a). On interval-valued nonlinear programming problems. Journal of Mathematical Analysis and Applications, 338, 299–316. https://doi.org/10.1016/j.jmaa.2007.05.023
Wu, H.C. (2008b). Wolfe duality for interval-valued optimization. Journal of Optimization Theory and Applications, 138, 497–509. https://doi.org/10.1007/s10957-008-9396-0
Wolfe, M., (2000). Interval mathematics, algebraic equations and optimization. Journal of Computational and Applied Mathematics, 124, 263–280.
https://doi.org/10.1016/S0377-0427(00)00421-0
Zabreiko, P. P., & Krasnoselski, M. A. (1971). Solvability of nonlinear operator equations. Functional Analysis and Its Applications, 5(3), 206-208.
https://doi.org/10.1007/BF01078126
Zhang, C., & Huang, N. (2022). On Ekeland’s variational principle for interval-valued functions with applications. Fuzzy Sets and Systems, 436,152–174. DOI:10.1016/j.fss.2021.10.003
Zhang, Z., Wang, X., & Lu, J. (2018). Multi-objective immune genetic algorithm solving nonlinear interval-valued programming. Engineering Applications of Artificial Intelligence, 67, 235–245. https://doi.org/10.1016/j.engappai.2017.10.004