Second order duality for nondifferentiable multiobjective programming problem involving (F, α, ρ, d)-V-type I functions

2009 ◽  
Vol 4 (2) ◽  
pp. 211-226 ◽  
Author(s):  
Anurag Jayswal ◽  
Dilip Kumar ◽  
Rajnish Kumar
Keyword(s):  
Programming Problem ◽  
Multiobjective Programming ◽  
Second Order ◽  
Type I ◽  
Second Order Duality ◽  
Multiobjective Programming Problem

Second Order Duality for Multiobjective Programming involving (F,ρ,σ) - Type I Functions

OPSEARCH ◽  
2000 ◽  
Vol 37 (4) ◽  
pp. 316-326 ◽  
Author(s):  
Manjari K. Srivastava ◽  
Misha G. Govil
Keyword(s):  
Multiobjective Programming ◽  
Second Order ◽  
Type I ◽  
Second Order Duality

Symmetric duality results for second-order nondifferentiable multiobjective programming problem

2019 ◽  
Vol 53 (2) ◽  
pp. 539-558 ◽  
Author(s):  
Ramu Dubey ◽  
Vishnu Narayan Mishra
Keyword(s):  
Programming Problem ◽  
Duality Theorem ◽  
Multiobjective Programming ◽  
Second Order ◽  
Weak Duality ◽  
Symmetric Duality ◽  
Numerical Examples ◽  
Duality Results ◽  
Duality Relations ◽  
Multiobjective Programming Problem

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.

Second-order duality for nondifferentiable multiobjective programming involving (Φ,ρ)-univexity

1970 ◽  
Vol 7 (1) ◽  
pp. 92-104
Author(s):  
Ganesh Kumar Thakur ◽  
Bandana Priya
Keyword(s):  
Key Words ◽  
Duality Theorem ◽  
Multiobjective Programming ◽  
Second Order ◽  
Dual Model ◽  
Weak Duality ◽  
Support Functions ◽  
Second Order Duality ◽  
Multiobjective Programming Problem ◽  
Quasi Convexity

The concepts of (Φ, ρ)-invexity have been given by Carsiti,Ferrara and Stefanescu[32]. We consider a second-order dual model associated to a multiobjective programming problem involving support functions and a weak duality result is established under appropriate second-order (Φ, ρ)-univexity conditions. AMS 2002 Subject Classification: 90C29; 90C30; 90C46. Key words: Second-order (Φ, ρ)-(pseudo/quasi)-convexity; multiobjective programming; second-order duality; duality theorem. DOI: http://dx.doi.org/ 10.3126/kuset.v7i1.5426 KUSET 2011; 7(1): 92-104  

scholarly journals Sufficiency and Duality in Nonsmooth Multiobjective Programming Problem under Generalized Univex Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Pallavi Kharbanda ◽  
Divya Agarwal ◽  
Deepa Sinha
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Multiobjective Programming ◽  
Generalized Functions ◽  
Sufficient Optimality Conditions ◽  
Type I ◽  
Duality Theorems ◽  
Nonsmooth Multiobjective Programming ◽  
Strong Converse ◽  
Multiobjective Programming Problem

We consider a nonsmooth multiobjective programming problem where the functions involved are nondifferentiable. The class of univex functions is generalized to a far wider class of (φ,α,ρ,σ)-dI-V-type I univex functions. Then, through various nontrivial examples, we illustrate that the class introduced is new and extends several known classes existing in the literature. Based upon these generalized functions, Karush-Kuhn-Tucker type sufficient optimality conditions are established. Further, we derive weak, strong, converse, and strict converse duality theorems for Mond-Weir type multiobjective dual program.

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