Second-order multiobjective programming problems and symmetric duality relations with $${G_{f}}$$ G f -bonvexity

OPSEARCH ◽  
2016 ◽  
Vol 54 (2) ◽  
pp. 365-387
Author(s):  
S. K. Gupta ◽  
Ramu Dubey ◽  
Indira P. Debnath
Keyword(s):  
Multiobjective Programming ◽  
Second Order ◽  
Symmetric Duality ◽  
Duality Relations ◽  
Multiobjective Programming Problems

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 symmetric duality in multiobjective programming

2003 ◽  
Vol 144 (3) ◽  
pp. 492-500 ◽  
Author(s):  
S.K. Suneja ◽  
C.S. Lalitha ◽  
Seema Khurana
Keyword(s):  
Multiobjective Programming ◽  
Second Order ◽  
Symmetric Duality ◽  
Second Order Symmetric Duality

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.

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