Nondifferentiable higher-order duality theorems for new type of dual model under generalized functions
AbstractThe motivation behind this article is to study a class of nondifferentiable multiobjective fractional programming problem in which each component of objective functions contains a term including the support function of a compact convex set. For a differentiable function, we consider a class of higher order pseudo quasi/ strictly pseudo quasi/weak strictly pseudo quasi- (V, ρ, d)-type-I convex functions. Under these the higher-order pseudo quasi/ strictly pseudo quasi/weak strictly pseudo quasi- (V, ρ, d)-type-I convexity assumptions, we prove the higher-order weak, higher-order strong and higher-order converse duality theorems related to efficient solution.
R. Dubey and S. K. Gupta, “Duality for a nondifferentiable multiobjective higher-order symmetric fractional programming problems with cone constraints”, Journal of nonlinear analysis and optimization, vol. 7, no, 1, pp. 1-15, 2016. [On line]. Available: https://bit.ly/2RRZaXg
R. Dubey and V. N. Mishra, “Symmetric duality results for second-order nondifferentiable multiobjective programming problem”, RAIRO - Operations research, vol. 53, no. 2, pp. 539–558, 2019, doi: 10.1051/ro/2019044.
R. Dubey, V. N. Mishra, and P. Tomar, “Duality relations for second-order programming problem under (G, αf)-bonvexity assumptions”, Asian-European journal of mathematics, Art ID. 2050044, 2020, doi: 10.1142/S1793557120500448.
T. R. Gulati and D. Agarwal, “Second-order duality in multiobjective programming involving (F, α, ρ, d)-V-type I functions”, Numerical functional analysis and optimization, vol. 28, no. 11-12, pp. 1263–1277, Oct. 2007, doi: 10.1080/01630560701749664.
T. R. Gulati and Geeta, “Duality in nondifferentiable multiobjective fractional programming problem with generalized invexity”, Journal of applied mathematics and computing, vol. 35, no. 1-2, pp. 103–118, Feb. 2009, doi: 10.1007/s12190-009-0345-3.
A. Jayswal, D. Kumar, and R. Kumar, “Second order duality for nondifferentiable multiobjective programming problem involving (F, α, ρ, d)-V-type I functions”, Optimization letters, vol. 4, no. 2, pp. 211–226, Nov. 2009, doi: 10.1007/s11590-009-0159-0.
A. Jayswal, I. M. Stancu-Minasian, and D. Kumar, “Higher-order duality for multiobjective programming problems involving (F, α, ρ, d)-V-type I functions”, Journal of mathematical modelling and algorithms in operations research, vol. 13, no. 2, pp. 125–141, Apr. 2013, doi: 10.1007/s10852-013-9224-x.
O. Mangasarian, “Second- and higher-order duality in nonlinear programming”, Journal of mathematical analysis and applications, vol. 51, no. 3, pp. 607–620, Sep. 1975, doi: 10.1016/0022-247X(75)90111-0.
S. K. Mishra, K. K. Lai, and V. Singh, “Optimality and duality for minimax fractional programming with support function under (C,α,ρ,d)-convexity”, Journal of computational and applied mathematics, vol. 274, pp. 1–10, Jan. 2015., doi: 10.1016/j.cam.2014.06.025.
S. K. Suneja, M. K. Srivastava, and M. Bhatia, “Higher order duality in multiobjective fractional programming with support functions”, Journal of mathematical analysis and applications, vol. 347, no. 1, pp. 8–17, Nov. 2008, doi: 10.1016/j.jmaa.2008.05.056.
X. M. Yang, K. L. Teo, and X. Q. Yang, “Higher-order generalized convexity and duality in nondifferentiable multiobjective mathematical programming”, Journal of mathematical analysis and applications, vol. 297, no. 1, pp. 48–55, Sep. 2004, doi: 10.1016/j.jmaa.2004.03.036.
J. Zhang, “Higher order convexity and duality in multiobjective programming problems”, in Progress in optimization. Contributions from australasia, vol. 30, A. Eberhard, R. Hill, D. Ralph, and B. M. Glover, Ed. Boston, MA: Springer, 1999, pp. 101–117, doi: 10.1007/978-1-4613-3285-5_6.
Vandana, R. Dubey, Deepmala, L. N. Mishra, and V. N. Mishra, “Duality Relations for a Class of a Multiobjective Fractional Programming Problem Involving Support Functions”, American journal of operations research, vol. 8, no. 4, pp. 294–311, Jul. 2018, doi: 10.4236/ajor.2018.84017.
R. Dubey, Vandana, and V. N. Mishra, “Second order multiobjective symmetric programming problem and duality relations under (F, Gf)-convexity”, Global journal of engineering science and researches, vol. 5, no. 8, pp. 187-199, 2018. [On line]. Available: https://bit.ly/30Ex5GM
R. Dubey, L. N. Mishra, and L. M. S. Ruiz, “Nondifferentiable G-Mond–Weir Type Multiobjective Symmetric Fractional Problem and Their Duality Theorems under Generalized Assumptions”, Symmetry, vol. 11, no. 11, Art. ID 1348, Jan. 2019, doi: 10.3390/sym11111348.
R. Dubey, L. N. Mishra, and C. Cesarano, “Multiobjective fractional symmetric duality in mathematical programming with (C,Gf)-invexity assumptions”, Axioms, vol. 8, no. 3, Art. ID. 97, Aug. 2019, doi: 10.3390/axioms8030097.
R. Dubey, L. N. Mishra, and R. Ali, “Special Class of Second-Order Non-Differentiable Symmetric Duality Problems with (G,αf)-Pseudobonvexity Assumptions”, Mathematics, vol. 7, no. 8, Art. ID 763, Aug. 2019, doi: 10.3390/math7080763.
Copyright (c) 2020 Ramu Dubey, Vishnu Narayan Mishra
This work is licensed under a Creative Commons Attribution 4.0 International License.