Necessary and Sufficient Optimality Conditions for Fractional Interval-Valued Variational Problems
DOI:
https://doi.org/10.2298/YJOR210815028RKeywords:
Variational programming problem, interval-valued programming problem, LU optimal solution, optimality, dualityAbstract
In this paper a special kind of variational programming problem involving fractional interval-valued objective function is considered. For such type of problem, insights into LU optimal solutions have been discussed. Using the LU optimal concept, we established optimality conditions for the considered problem. Further, We formulated a Mond-Weir dual problem and discussed appropriate duality theorems for the relationship between dual and primal problems.References
Barbagallo, L. Mallozzi, and M. Thera, “Preface: Special issue on recent advances in variational calculus: Principles, tools and applications”, Journal of Optimization Theory and Applications, vol. 182, pp. 1-3, 2019.
L. Blasi, S. Barbato, and M. Mattei, “A particle swarm approach for flight path optimization in a constrained environment”, Aerospace Science and Technology, vol. 26, no. 1, pp. 128- 137, 2013.
R. Esmaelzadeh, “Low-thrust orbit transfer optimization using a combined method”, International Journal of Computer Applications, vol. 89, pp. 20-24, 2014.
S. Khardi, “Aircraft flight path optimization the Hamilton-Jacobi-Bellman considerations”, Applied Mathematical Sciences, vol. 6, pp. 1221-1249, 2012.
M. A. Hanson, “Bounds for functionally convex optimal control problems”, Journal of Mathematical Analysis and Applications, vol. 8, pp. 84-89, 1964.
B. Mond, and M. A. Hanson, “Duality for variational problems”, Journal of Mathematical Analysis and Applications, vol. 18, pp. 355-364, 1967.
D. Bhatia, and P. Kumar, “Multiobjective control problem with generalized invexity”, Journal of Mathematical Analysis and Applications, vol. 189, pp. 676-692, 1995.
P. Kumar, and J. Dagar, “Optimality and duality for multio-bjective semi-infinite variational problem using higher-order B-type I functions”, Journal of the Operations Research Society of China, (2019) Doi:10.1007/s40305-019-00269-6.
I. Ahmad, A. Jayswal, S. Al-Homidan, and J. Banerjee, “Sufficiency and duality in intervalvalued variational programming”, Neural Computer Applications, vol. 31, no. 8, pp. 4423- 4433, 2019.
I. Ahmad, and S. Sharma, “Sufficiency and duality for multiobjective variational control problems with generalized (F, α, ρ, θ)-V -convexity”, Nonlinear Analysis, vol. 72, pp. 2564- 2579, 2010.
S. Mititelu, and I. M. Stancu-Minastan, “Efficiency and duality for multiobjective fractional variational problems with (ρ, b)-quasi-invexity”, Yugoslav Journal of Operations Research, vol. 19, pp. 85-99, 2009.
C. Nahak, and S. Nanda, “Sufficient optimality criteria and duality for multiobjective variational control problems with V -invexity”, Nonlinear Analysis , vol. 66, pp. 1513-1525, 2007.
B. Sharma, and P. Kumar, “Necessary optimality conditions for multiobjective semi-infinite variational problem”, American Journal of Operations Research, vol. 6, pp. 36-43, 2016.
Alkhazaleh, “The Multi-interval-valued fuzzy soft set with application in decision making”, Applied Mathematics, vol. 6, pp. 1250-1262, 2015.
B. Chetia, and P. K. Das, “An Application of interval valued fuzzy soft set in medical diagnosis”, International Journal of Contemporary Mathematical Sciences, vol. 5 no. 38, pp. 1887-1894, 2010.
D. Yin, “Application of interval valued fuzzy linear programming for stock portfolio optimization”, Applied Mathematics, vol. 9, pp. 101-113, 2018.
A. K. Bhurjee, and G. Panda, “Efficient solution of interval optimization problem”, Mathematical Methods of Operations Research, vol. 76, pp. 273-288, 2012.
S. Deepak, B. Ahmad Dar, and D. S. Kim, “sufficiency and duality in non-smooth itervalvalued programming problems”, Journal of Industrial and Management Optimization, vol. 15, no. 2, pp. 647-665, 2019.
S. Chanas, and D. Kuchta, “Multi-objective programming in optimization of interval objective functions-a generalized approach”, European Journal of Operational Research, vol. 94, pp. 594-598, 1996.
C. Jiang, X. Han, and G. P. Liu, “A nonlinear interval number programming method for uncertain optimization problems”, European Journal of Operational Research, vol. 188, pp. 1-13, 2008.
S. -T. Liu, “Polynomial geometric programming with interval exponents and coefficients”, European Journal of Operational Research, vol. 186, pp. 7-27, 2008.
Y. An, G. Ye, D. Zhao, and W. Liu, “Hermite-Hadamard type inequalities for interval (h1, h2)-convex functions”, Mathematics, vol. 7, Art. ID 436, 2019.
K. Kummari, and I. Ahmad, “Sufficient optimality conditions and duality for non-smooth interval-valued optimization problems via L-invex-infine functions”, Politehnica University of Bucharest Scientific Bulletin, Series A, Applied Mathematics and Physics, vol. 82, no. 1, pp. 45-54, 2020.
K. Kummari, I. Ahmad, and S. Al-Homidin, “Sufficiency and duality for interval-valued optimization problems with vanishing constraints using weak constraint qualifications”, International Journal of Analysis and Applications, vol. 18, pp. 784-798, 2020.
R. Osuna-Gómez, B. Hernández-Jiménez, and Chalco-Cano and Y. G. Ruiz-Garzón,“New efficiency conditions for multiobjective interval-valued programming problems”, Information Sciences, vol. 420, pp. 235-248, 2017.
L.Wang, G. Yang, H. Xiao, Q. Sun, and J. Ge, “Interval optimization for structural dynamic responses of an artillery system under uncertainty”, Engineering Optimization, vol. 52, pp. 343-366, 2020.
H. C. Wu, “Solving the interval-valued optimization problems based on the concept of null set”, Journal of Industrial and Management Optimization, vol. 14, no. 3, pp. 1157-1178, 2018.
T. Antczak, and A. Pitea, “Parmetric approach to multitime multiobjective fractional variational problems under (F,ρ)-convexity”, Optimal Control Applications and Methods, vol. 37, pp. 831-847, 2016.
S. Mititelu, and M. Postolache, “Efficiency and duality for multitime vector fractional variational problems on manifolds”, Journal of Advanced Mathematical Studies, vol. 4, no. 2, 2011.
H.-C. Lai, “Sufficiency and duality of fractional integral programming with generalized invexity”, Taiwanese Journal of Mathematics, vol. 10, no. 6, pp. 1685-1695, 2006.
S. Treanta, “Sufficiency conditions associated with a multidimensional multiobjective fractional variational problem”, Journal of Multidisciplinary Modelling and Optimization , vol. 1, no. 1, pp. 1-13, 2018.
C. R. Bector, S. Chandra, and I. Husain, “Optimality conditions and duality in subdifferentiable multiobjective fractional programming”, Journol of Optimization Theory and Applications, vol. 79, pp. 105-125, 1993.
G. J. Zalmai, “Optimality conditions and duality models for a class of nonsmooth constrained fractional variational problems”, Optimization, vol. 30, pp. 15-51, 1994.
S. Chandra, B. D. Craven, and I. Husain, “Continuous programming containing arbitrary norms”, Journal of the Australian Mathematical Society, vol. 39, pp. 28-38, 1985.
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