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.

Duality relations for second-order programming problem under (G,αf)-bonvexity assumptions

2018 ◽  
Vol 13 (02) ◽  
pp. 2050044 ◽  
Author(s):  
Ramu Dubey ◽  
Vishnu Narayan Mishra ◽  
Puneet Tomar
Keyword(s):  
Programming Problem ◽  
Duality Theorem ◽  
Optimization Problem ◽  
Second Order ◽  
Dual Model ◽  
Weak Duality ◽  
Numerical Examples ◽  
Duality Results ◽  
Duality Relations ◽  
Definition Of

In this paper, we introduce the definition of [Formula: see text]-bonvex/[Formula: see text]-pseudobonvex functions and to show the existence of such functions, we construct nontrivial numerical examples. In the next section, we formulate a pair of second-order symmetric dual model in optimization problem and proved the duality results under [Formula: see text]-bonvexity/[Formula: see text]-pseudobonvexity assumptions. Further, we also construct nontrivial concrete examples which justifying definitions as well as the weak duality theorem presented in the paper.

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 Special Class of Second-Order Non-Differentiable Symmetric Duality Problems with (G,αf)-Pseudobonvexity Assumptions

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 763 ◽  
Author(s):  
Ramu Dubey ◽  
Lakshmi Narayan Mishra ◽  
Rifaqat Ali
Keyword(s):  
Special Class ◽  
Second Order ◽  
Weak Duality ◽  
Symmetric Duality ◽  
Numerical Examples ◽  
Duality Result ◽  
Numerical Example ◽  
Duality Relations ◽  
Dual Models

In this paper, we introduce the various types of generalized invexities, i.e., α f -invex/ α f -pseudoinvex and ( G , α f ) -bonvex/ ( G , α f ) -pseudobonvex functions. Furthermore, we construct nontrivial numerical examples of ( G , α f ) -bonvexity/ ( G , α f ) -pseudobonvexity, which is neither α f -bonvex/ α f -pseudobonvex nor α f -invex/ α f -pseudoinvex with the same η . Further, we formulate a pair of second-order non-differentiable symmetric dual models and prove the duality relations under α f -invex/ α f -pseudoinvex and ( G , α f ) -bonvex/ ( G , α f ) -pseudobonvex assumptions. Finally, we construct a nontrivial numerical example justifying the weak duality result presented in the paper.

scholarly journals Symmetric duality in complex spaces over cones

2021 ◽  
pp. 4-4
Author(s):  
Izhar Ahmad ◽  
Divya Agarwal ◽  
Kumar Gupta
Keyword(s):  
Mathematical Programming ◽  
Duality Theory ◽  
Optimization Theory ◽  
Second Order ◽  
Symmetric Duality ◽  
Polyhedral Cones ◽  
Complex Spaces ◽  
Duality Results ◽  
Duality Relations

Duality theory plays an important role in optimization theory. It has been extensively used for many theoretical and computational problems in mathematical programming. In this paper duality results are established for first and second order Wolfe and Mond-Weir type symmetric dual programs over general polyhedral cones in complex spaces. Corresponding duality relations for nondifferentiable case are also stated. This work will also remove inconsistencies in the earlier work from the literature.

scholarly journals Higher-order symmetric duality in nondifferentiable multiobjective fractional programming problem over cone contraints

2020 ◽  
Vol 8 (1) ◽  
pp. 187-205 ◽  
Author(s):  
Ramu Dubey ◽  
Deepmala ◽  
Vishnu Narayan Mishra
Keyword(s):  
Programming Problem ◽  
Fractional Programming ◽  
Higher Order ◽  
Multiobjective Fractional Programming ◽  
Symmetric Duality ◽  
Numerical Examples ◽  
Fractional Programming Problem ◽  
Multiobjective Fractional Programming Problem ◽  
Duality Relations ◽  
Definition Of

In this paper, we introduce the definition of higher-order K-(C, α, ρ, d)-convexity/pseudoconvexity over cone and discuss a nontrivial numerical examples for existing such type of functions. The purpose of the paper is to study higher order fractional symmetric duality over arbitrary cones for nondifferentiable Mond-Weir type programs under higher- order K-(C, α, ρ, d)-convexity/pseudoconvexity assumptions. Next, we prove appropriate duality relations under aforesaid assumptions.

scholarly journals Duality for a class of nonsmooth multiobjective programming problems using convexificators

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 489-498 ◽  
Author(s):  
Anurag Jayswal ◽  
Krishna Kummari ◽  
Vivek Singh
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Duality Results ◽  
Nonsmooth Multiobjective Programming ◽  
Multiobjective Programming Problem ◽  
Multiobjective Programming Problems ◽  
Dual Models

As duality is an important and interesting feature of optimization problems, in this paper, we continue the effort of Long and Huang [X. J. Long, N. J. Huang, Optimality conditions for efficiency on nonsmooth multiobjective programming problems, Taiwanese J. Math., 18 (2014) 687-699] to discuss duality results of two types of dual models for a nonsmooth multiobjective programming problem using convexificators.

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