In this article, for a differentiable function , we introduce the definition of the higher-order -invexity. Three duality models for a multiobjective fractional programming problem involving nondifferentiability in terms of support functions have been formulated and usual duality relations have been established under the higher-order -invex assumptions.
References
[1]
Mangasarian, O.L. (1975) Second and Higher-Order Duality in Nonlinear Programming. Journal of Mathematical Analysis and Applications, 51, 607-620. https://doi.org/10.1016/0022-247X(75)90111-0
[2]
Egudo, R.R. (1988) Multiobjective Fractional Duality. Bulletin of the Australian Mathematical Society, 37, 367-378. https://doi.org/10.1017/S0004972700026988
[3]
Gulati, T.R. and Agarwal, D. (2008) Optimality and Duality in Nondifferentiable Multiobjective Mathematical Programming Involving Higher Order (F,α,ρ,d) - Type I Functions. Journal of Applied Mathematics and Computing, 27, 345-364. https://doi.org/10.1007/s12190-008-0069-9
[4]
Chen, X. (2004) Higher-Order Symmetric Duality in Nondifferentiable Multiobjective Programming Problems. Journal of Mathematical Analysis and Applications, 290, 423-435. https://doi.org/10.1016/j.jmaa.2003.10.004
[5]
Suneja, S.K., Srivastava, M.K. and Bhatia, M. (2008) Higher Order Duality in Multiobjective Fractional Programming with Support Functions. Journal of Mathematical Analysis and Applications, 347, 8-17. https://doi.org/10.1016/j.jmaa.2008.05.056
[6]
Dubey, R. and Gupta, S.K. (2016) Duality for a Nondifferentiable Multiobjective Higher-Order Symmetric Fractional Programming Problems with Cone Constraints. Journal of Nonlinear Analysis and Optimization: Theory and Applications, 7, 1-15.
[7]
Gupta, S.K., Dubey, R. and Debnath, I.P. (2017) Second-Order Multiobjective Programming Problems and Symmetric Duality Relations with Gƒ-Bonvexity. OPSEARCH, 54, 365-387. https://doi.org/10.1007/s12597-016-0280-7
[8]
Kuk, H., Lee, G.M. and Kim, D.S. (1998) Nonsmooth Multiobjective Programs with V-ρ-Invexity. Indian Journal of Pure and Applied Mathematics, 29, 405-412.
[9]
Jeyakumar, V. and Mond, B. (1992) On Generalised Convex Mathematical Programming. Journal of the Australian Mathematical Society Series B, 34, 43-53. https://doi.org/10.1017/S0334270000007372
[10]
Pandey, S. (1991) Duality for Multiobjective Fractional Programming Involving Generalized η-Bonvex Functions. OPSEARCH, 28, 31-43.
[11]
Gulati, T.R. and Geeta (2011) Duality in Nondifferentiable Multiobjective Fractional Programming Problem with Generalized Invexity. Journal of Applied Mathematics and Computing, 35, 103-118. https://doi.org/10.1007/s12190-009-0345-3
[12]
Gupta, S.K., Kailey, N. and Sharma, M.K. (2010) Multiobjective Second-Order Nondifferentiable Symmetric Duality Involving (F,α,ρ,d) -Convex Function. Journal of Applied Mathematics and Informatics, 28, 1395-1408.
[13]
Dubey, R., Gupta, S.K. and Khan, M.A. (2015) Optimality and Duality Results for a Nondifferentiable Multiobjective Fractional Programming Problem. Journal of Inequalities and Applications, 354. https://doi.org/10.1186/s13660-015-0876-0
[14]
Reddy, L.V. and Mukherjee, R.N. (1999) Some Results on Mathematical Programming with Generalized Ratio Invexity. Journal of Mathematical Analysis and Applications, 240, 299-310. https://doi.org/10.1006/jmaa.1999.6334
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, we introduce the definition of the higher-order ![\"\"](\"Edit_1f0d9209-a7b7-46e4-b4ac-f5f9360b3c3b.png\")
-invexity. Three duality models for a multiobjective fractional programming problem involving nondifferentiability in terms of support functions have been formulated and usual duality relations have been established under the higher-order ![\"\"](\"Edit_4ece95c2-7bc1-42cf-8d33-5afa5734925a.png\")
-invex assumptions.
