Symmetric duality results for second-order nondifferentiable multiobjective programming problem
RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 2, pp. 539-558.

In this article, we study the existence of Gf-bonvex/Gf-pseudo-bonvex functions and construct various nontrivial numerical examples for the existence of such type of functions. Furthermore, we formulate Mond-Weir type second-order nondifferentiable multiobjective programming problem and give a nontrivial concrete example which justify weak duality theorem present in the paper. Next, we prove appropriate duality relations under aforesaid assumptions.

DOI : 10.1051/ro/2019044
Classification : 90C26, 90C3, 90C32, 90C46
Mots-clés : Symmetric duality, nondifferentiable, support function, Gf -bonvexity/Gf -pseudo-bonvexity, Mond-Weir type model
Dubey, Ramu 1 ; Mishra, Vishnu Narayan 1

1 
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     title = {Symmetric duality results for second-order nondifferentiable multiobjective programming problem},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {539--558},
     publisher = {EDP-Sciences},
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Dubey, Ramu; Mishra, Vishnu Narayan. Symmetric duality results for second-order nondifferentiable multiobjective programming problem. RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 2, pp. 539-558. doi : 10.1051/ro/2019044. https://www.numdam.org/articles/10.1051/ro/2019044/

[1] T. Antczak , New optimality conditions and duality results of G-type in differentiable mathematical programming. Nonlinear Anal. 66 (2007) 1617–1632. | Zbl

[2] T. Antczak , On G-invex multiobjective programming. Part I. Optimality. J. Global Optim. 43 (2009) 97–109. | Zbl

[3] D. Bhatia and P.K. Garg , (V, ρ) invexity and non-smooth multiobjective programming. RAIRO: OR 32 (1998) 399–414.

[4] X.H. Chen , Higher-order symmetric duality in nondifferentiable multiobjective programming problems. J. Math. Anal. Appl. 290 (2004) 423–435. | Zbl

[5] R. Dubey and S.K. Gupta , Duality for a nondifferentiable multiobjective higher-order symmetric fractional programming problems with cone constraints. J. Non-linear Anal. Optim. 7 (2016) 1–15. | Zbl

[6] R. Dubey , V.N. Vandana and V.N. Mishra , Second-order multiobjective symmetric programming problem and duality relations under (F, G f ) convexity. Global J. Eng. Sci. Res. 5 (2018) 187–199.

[7] R. Dubey , L.N. Mishra and V.N. Mishra , Duality relations for a class of a multiobjective fractional program- ming problem involving support functions. Am. J. Oper. Res. 8 (2018) 294–311.

[8] R. Dubey , V.N. Mishra and P. Tomar , Duality relations for second-order programming problem under (G, α f )-bonvexity assumptions. Asian-Eur. J. Math. 13 (2020) 1–17.

[9] M. Ferrara and M.V. Stefaneseu , Optimality conditions and duality in multiobjective programming with (ϕ, ρ)-invexity. Yugoslav J. Oper. Res. 18 (2008) 153–165. | Zbl

[10] T.R. Gulati and S.K. Gupta , Wolfe type second-order symmetric duality in nondifferentiable programming. J. Math. Anal. Appl. 310 (2005) 247–253. | Zbl

[11] T.R. Gulati , H. Saini and S.K. Gupta , Second-order multiobjective symmetric duality with cone constraints. Eur. J. Oper. Res. 205 (2010) 247–252. | Zbl

[12] A. Jayswal , R. Kumar and D. Kumar , Multiobjective fractional programming problems involving (p, r)−ρ−(η, θ)-invex function. J. Appl. Math. Comput. 39 (2012) 35–51. | Zbl

[13] Y.M. Kang , D.S. Kim and M.H. Kim , Optimality conditions of G-type in locally Lipchitz multiobjective programming. Vietnam J. Math. 40 (2012) 275–285. | Zbl

[14] S. Khurana , Symmetric duality in multiobjective programming involving generalized cone-invex functions. Eur. J. Oper. Res. 165 (2005) 592–597. | Zbl

[15] P. Mandal and C. Nahak , Symmetric duality with (p, r)−ρ−(η, θ)-invexity. Int. J. Pure Appl. Math. 217 (2011) 8141–8148. | Zbl

[16] O.L. Mangasarian , Second and higher order duality in nonlinear programming. J. Math. Anal. Appl. 51 (1975) 607–620. | Zbl

[17] S.K. Mishra and K.K. Lai , Second-order symmetric duality in multiobjective programming involving generalized cone-invex functions. Eur. J. Oper. Res. 178 (2007) 20–26. | Zbl

[18] N.G. Reuda , M.A. Hanson and C. Singh , Optimality and duality with generalized convexity. J. Optim. Theory Appl. 86 (1995). | Zbl

[19] S.K. Suneja , S. Aggarwal and S. Davar , Multiobjective symmetric duality involving cones. Eur. J. Oper. Res. 141 (2002) 471–479. | Zbl

[20] S.K. Suneja , C.S. Lalitha and S. Khurana , Second order symmetric duality in multiobjective programming. Eur. J. Oper. Res. 144 (2003) 492–500. | Zbl

[21] M.V. Stefaneseu and M. Ferrara , Multiobjective programming with new invexities. Optim. Lett. 7 (2013) 855–870. | Zbl

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