Generalized $G$-Wolfe type fractional symmetric duality theorems over arbitrary cones under $(G,\rho,\theta)$-invexity assumptions

Document Type : Research Paper


1 Department of Mathematics, J.C. Bose University of Science and Technology, YMCA, Faridabad-121006, Haryana, India

2 Department of Mathematics, Noida Institute of Engineering & Technology, Greater Noida, India

3 Department of Mathematics, School of Basic Sciences and Research, Sharda University, India

4 Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur -484 887, Madhya Pradesh, India


In this paper, we introduce the concept of $(G,\rho,\theta)$-invexity/pseudoinvexity. We formulate duality outcomes for $G$-Wolfe-type fractional symmetric dual programs over arbitrary cones. In the final  section, we discuss  the  duality theorems under  $(G,\rho,\theta)$-invexity/ $(G,\rho,\theta)$-psedoinvexity assumptions.


[1] B. Mond, A class of nondifferentiable fractional programming problems, ZAMM., 58 (1978) 337–341.
[2] J. Zhang and B. Mond, Duality for a class of nondifferentiable fractional programming problems. Int. J. Mang.
Sys. 14 (1998) 71–88.
[3] DS. Kim, YB. Yun and WJ. Lee, Multiobjective Symmetric duality with cone constraints, Eur. J. Oper. Res. 107
(1998) 686–691.
[4] G. Devi, Symmetric duality for nonlinear programming problem involving η-convex functions, Eur. J. Oper. Res.
104 (1998) 615–621.
[5] X. Chen, Sufficient conditions and duality for a class of multiobjective fractional programming problems with
higher-order (F, α, ρ, d)-convexity, J. Appl. Math. Comput. 28 (2008) 107–121.
[6] XM. Yang, XQ. Yang, KL. Teo and SH. Hou, Multiobejctive second order symmetric duality with F-convexity,
Eur. J. Oper. Res. 165 (2005) 585–591.
[7] C. Gutierrez, B. Jimenez, V. Novo and G. Ruiz-Garzon, Efficiency through variational-like inequalities with
lipschitz functions, Appl. Math. Comput. 259 (2015) 438–449.
[8] S. Khurana, Symmetric duality in multiobjective programming involving generalized cone-invex functions, Eur. J.
Oper. Res., 165(2005) 592–597.
[9] DB. Ojha, On second-order symmetric duality for a class of multiobjective fractional programming problem,
Tamkang J. Math. 43 (2012) 267–279.
[10] R. Dubey and VN. Mishra, Symmetric duality results for second-order nondifferentiable multiobjective programming problem, RAIRO-Oper. Res. 53 (2019) 539–558.
[11] R. Dubey, Deepmala and VN. Mishra, Higher-order symmetric duality in nondifferentiable multiobjective fractional programming problem over cone contraints, Stat., Optim. Inf. Comput. 8 (2020) 187–205.
[12] R. Dubey and VN. Mishra, Nondifferentiable higher-order duality theorems for new type of dual model under
generalized functions, Proyecciones journal of Math. 39 (2020) 15–29.
[13] IM. Stancu-Minasian, A seventh bibliography of fractional programming, Adv. Model. Optim. 15 (2013) 309–386.
[14] G. Ying, Higher-order symmetric duality for a class of multiobjective fractional programming problems, Adv.
Model. Optim. 142 (2012).
[15] M. Bhatia, Higher order duality in vector optimization over cones, J. Math. Anal. Appl. 71 (1979) 251–262.
[16] M. Schechter, More on subgradient duality. Optim. Lett. 6 (2012) 17–3
Volume 12, Special Issue
December 2021
Pages 643-651
  • Receive Date: 25 June 2020
  • Revise Date: 08 December 2020
  • Accept Date: 25 December 2020