Nondifferentiable G-Mond-Weir Type Multiobjective Symmetric Fractional Problem and Their Duality Theorems under Generalized Assumptions

In this article, a pair of nondifferentiable second-order symmetric fractional primal-dual model (G-Mond–Weir type model) in vector optimization problem is formulated over arbitrary cones. In addition, we construct a nontrivial numerical example, which helps to understand the existence of such type of functions. Finally, we prove weak, strong and converse duality theorems under aforesaid assumptions.

[1]  R. Dubey,et al.  Special Class of Second-Order Non-Differentiable Symmetric Duality Problems with (G,αf)-Pseudobonvexity Assumptions , 2019, Mathematics.

[2]  Surjeet Kaur Suneja,et al.  Multiobjective symmetric duality involving cones , 2002, Eur. J. Oper. Res..

[3]  Shelby Brumelle,et al.  Duality for Multiple Objective Convex Programs , 1981, Math. Oper. Res..

[4]  Vishnu Narayan Mishra,et al.  Duality Relations for a Class of a Multiobjective Fractional Programming Problem Involving Support Functions , 2018 .

[5]  Do Sang Kim,et al.  Multiobjective symmetric duality with cone constraints , 1998, Eur. J. Oper. Res..

[6]  C. S. Lalitha,et al.  Second order symmetric duality in multiobjective programming , 2003, Eur. J. Oper. Res..

[7]  Tadeusz Antczak New optimality conditions and duality results of G type in differentiable mathematical programming , 2007 .

[8]  Tadeusz Antczak On G-invex multiobjective programming. Part II. Duality , 2009, J. Glob. Optim..

[9]  Xiaoyan Gao Sufficiency in Multiobjective Programming under Second-order B - (p,r) - V - type I Functions , 2014 .

[10]  Olvi L. Mangasarian,et al.  Second- and higher-order duality in nonlinear programming☆ , 1975 .

[11]  Tadeusz Antczak On G-invex multiobjective programming. Part I. Optimality , 2009, J. Glob. Optim..

[12]  Seema Khurana,et al.  Symmetric duality in multiobjective programming involving generalized cone-invex functions , 2005, Eur. J. Oper. Res..

[13]  Panos M. Pardalos,et al.  A survey of recent developments in multiobjective optimization , 2007, Ann. Oper. Res..

[14]  Ramu Dubey,et al.  Symmetric duality results for second-order nondifferentiable multiobjective programming problem , 2019, RAIRO Oper. Res..