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A new approach for solving multi-objective interval-valued variational problems and its applications | ||
Communications in Combinatorics and Optimization | ||
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 06 آذر 1403 اصل مقاله (443.9 K) | ||
نوع مقاله: Original paper | ||
شناسه دیجیتال (DOI): 10.22049/cco.2024.29824.2173 | ||
نویسندگان | ||
Shubham Singh؛ Shalini Jha* | ||
School of Advanced Sciences, VIT-AP University, Amaravati, Vijaywada, 522237, Andhra Pradesh, India | ||
چکیده | ||
This study focuses on one of the methods for solving a nonlinear multiobjective convex interval-valued variational problem. Namely, the weighting method is used to find its weakly $LU$-efficient solution and $LU$-efficient solution. Therefore, the weighted variational problem is introduced for the given nonlinear multiobjective interval-valued variational problem. Then, under appropriate convexity assumptions, the equivalance between a (weakly) $LU$-efficient solution of the original nonlinear multiobjective interval-valued variational problem and an optimal solution of its associated weighting variational problem is established. | ||
کلیدواژهها | ||
multiobjective interval-valued variational problem؛ weighting method, (weakly) LU-efficient solution؛ convex interval-valued functional | ||
مراجع | ||
[1] B. Aghezzaf and K. Khazafi, Sufficient conditions and duality for multiobjective variational problems with generalized B-invexity, Control Cybernet. 33 (2004), no. 1, 113–126.
[2] I. Ahmad, A. Jayswal, S. Al-Homidan, and J. Banerjee, Sufficiency and duality in interval-valued variational programming, Neural Comput. Appl. 31 (2019), no. 8, 4423–4433. https://doi.org/10.1007/s00521-017-3307-y
[3] I. Ahmad, D. Singh, and B.A. Dar, Optimality conditions in multiobjective programming problems with interval valued objective functions, Control Cybernet. 44 (2015), no. 1, 19–45.
[4] G. Alefeld and J. Herzberger, Introduction to Interval Computations, Academic press, 2012.
[5] T. Antczak, The F-objective function method for differentiable interval-valued vector optimization problems., J. Ind. Manag. Optim. 17 (2021), no. 5, 2761–2782. https://doi.org/10.3934/jimo.2020093
[6] T. Antczak, Weighting method for convex vector interval-valued optimization problems, Politehn. Univ. Bicharest Sci. Bull. Ser. A Appl. Math. Phys 84 (2022), no. 2, 155–162.
[7] T. Antczak and M.A. Jiménez, Sufficient optimality criteria and duality for multiobjective variational control problems with $B-(p, r)$-invex functions., Opuscula Math. 34 (2014), no. 4, 665–682. http://dx.doi.org/10.7494/OpMath.2014.34.4.665
[8] M. Arana-Jiménez, R. Osuna-Gómez, G. Ruiz-Garzón, and M. Rojas-Medar, On variational problems: Characterization of solutions and duality, J. Math. Anal. Appl. 311 (2005), no. 1, 1–12. https://doi.org/10.1016/j.jmaa.2004.12.001
[9] A. Charnes, F. Granot, and F. Phillips, An algorithm for solving interval linear programming problems, Oper. Res. 25 (1977), no. 4, 688–695. https://doi.org/10.1287/opre.25.4.688
[10] M. Ciontescu and S. Treanţă, On some connections between interval-valued variational control problems and the associated inequalities, Results Control Optim. 12 (2023), Article ID: 100300. https://doi.org/10.1016/j.rico.2023.100300
[11] I.P. Debnath and N. Pokharna, On optimality and duality in interval-valued variational problem with $B-(p, r)$-invexity, RAIRO Oper. Res. 55 (2021), no. 3, 1909–1932. https://doi.org/10.1051/ro/2021088
[12] F. Giannessi, Theorems of the alternative and optimality conditions, J. Optim. Theory Appl. 42 (1984), no. 3, 331–365. https://doi.org/10.1007/BF00935321
[13] G. Giorgi, Again on the Farkas theorem and the Tucker key theorem proved easily, Tech. report, University of Pavia, Department of Economics and Management, 2014.
[14] M.A. Hanson, Bounds for functionally convex optimal control problems, J. Math. Anal. Appl. 8 (1964), no. 1, 84–89. https://doi.org/10.1016/0022-247X(64)90086-1
[15] H. Ishibuchi and H. Tanaka, Multiobjective programming in optimization of the interval objective function, European J. Oper. Res. 48 (1990), no. 2, 219–225. https://doi.org/10.1016/0377-2217(90)90375-L.
[16] M. Jana and G. Panda, Solution of nonlinear interval vector optimization problem, Oper. Res. 14 (2014), no. 1, 71–85. https://doi.org/10.1007/s12351-013-0137-2
[17] A. Jayswal, T. Antczak, and S. Jha, On equivalence between a variational problem and its modified variational problem with the $\eta$-objective function under invexity, Int. Trans. Oper. Res. 26 (2019), no. 5, 2053–2070. https://doi.org/10.1111/itor.12377
[18] A. Jayswal and A. Baranwal, Relations between multidimensional interval-valued variational problems and variational inequalities, Kybernetika 58 (2022), no. 4, 564–577. http://dx.doi.org/10.14736/kyb-2022-4-0564
[19] A. Jayswal, I.M. Stancu-Minasian, and S. Choudhury, Second order duality for variational problems involving generalized convexity, Opsearch 52 (2015), no. 3, 582–596. https://doi.org/10.1007/s12597-014-0195-0
[20] S. Jha, P. Das, and T. Antczak, Exponential type duality for $\eta$-approximated variational problems, Yugosl. J. Oper. Res. 30 (2019), no. 1, 19–43.
[21] S. Jha, P. Das, and S. Bandhyopadhyay, Characterization of lu-efficiency and saddle-point criteria for F-approximated multiobjective interval-valued variational problems, Results Control Optim. 4 (2021), Article ID: 100044. https://doi.org/10.1016/j.rico.2021.100044
[22] S. Khatri and A.K. Prasad, Duality for a fractional variational formulation using $\eta$-approximated method, Kybernetika 59 (2023), no. 5, 700–722. http://dx.doi.org/10.14736/kyb-2023-5-0700
[23] R.E. Moore, Interval Analysis, Prentice-Hall, New Jersey, 1966.
[24] R.E. Moore, Methods and Applications of Interval Analysis, SIAM, 1979.
[25] R.E. Moore, R.B. Kearfott, and M.J. Cloud, Introduction to Interval Analysis, SIAM, 2009.
[26] C. Nahak and N. Behera, Optimality conditions and duality for multiobjective variational problems with generalized $\rho-(\eta, \teta)-B$-Type-I functions, J. Control Sci. Eng. 2011 (2011), no. 1, Article ID: 497376. https://doi.org/10.1155/2011/497376
[27] F.L. Pereira, Control design for autonomous vehicles: A dynamic optimization perspective, Eur. J. Control 7 (2001), no. 2–3, 178–202. https://doi.org/10.3166/ejc.7.178-202.
[28] F.L. Pereira, A maximum principle for impulsive control problems with state constraints, Comput. Math. Appl 19 (2000), no. 2, 137–155.
[29] B.J. Rani and K. Kummari, Duality for fractional interval-valued optimization problem via convexificator, Opsearch 60 (2023), no. 1, 481–500.
[30] S. Sharma, A. Jayswal, and S. Choudhury, Sufficiency and mixed type duality for multiobjective variational control problems involving $\alpha$-V-univexity, Evol. Equ. Control Theory 6 (2017), no. 1, Article ID: 93. https://doi.org/10.3934/eect.2017006
[31] S. Treanţă, Characterization results of solutions in interval-valued optimization problems with mixed constraints, J. Global Optim. 82 (2022), no. 4, 951–964. https://doi.org/10.1007/s10898-021-01049-4
[32] S. Treanţă, On a class of interval-valued optimization problems, Contin. Mech. Thermodyn. 34 (2022), no. 2, 617–626. https://doi.org/10.1007/s00161-022-01080-0
[33] S. Treanţă and M. Ciontescu, On optimal control problems with generalized invariant convex interval-valued functionals, J. Ind. Manag. Optim. 20 (2024), no. 11, 3317–3336. https://doi.org/10.3934/jimo.2024055
[34] H.C. Wu, The Karush–Kuhn–Tucker optimality conditions in multiobjective programming problems with interval-valued objective functions, European J. Oper. Res. 196 (2009), no. 1, 49–60. https://doi.org/10.1016/j.ejor.2008.03.012
[35] H.C. Wu, Solving the interval-valued optimization problems based on the concept of null set, J. Ind. Manag. Optim. 14 (2018), no. 3, 1157–1178. https://doi.org/10.3934/jimo.2018004 | ||
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