scholarly journals A class of second order nondifferentiable symmetric duality relations under generalized assumptions

2020 ◽  
Vol 21 (02) ◽  
pp. 120-126 ◽  
Author(s):  
Ramu Dubey ◽  
Vandana ◽  
Vishnu Narayan Mishra ◽  
Seda Karateke
Keyword(s):  
Second Order ◽  
Symmetric Duality ◽  
Duality Relations

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.

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.

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.

Multiobjective second-order mixed symmetric duality with a square root term

2012 ◽  
Vol 218 (14) ◽  
pp. 7602-7613 ◽  
Author(s):  
S.K. Gupta ◽  
N. Kailey
Keyword(s):  
Second Order ◽  
Square Root ◽  
Symmetric Duality ◽  
Root Term
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