scholarly journals New class of G-Wolfe-type symmetric duality model and duality relations under Gf$G_{f}$-bonvexity over arbitrary cones

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ramu Dubey ◽  
Arvind Kumar ◽  
Rifaqat Ali ◽  
Lakshmi Narayan Mishra
Keyword(s):  
Symmetric Duality ◽  
New Class ◽  
Duality Relations ◽  
Duality Model

scholarly journals Symmetric duality for Bonvex multiobjective fractional continuous time programming problems

2010 ◽  
Vol 7 (2) ◽  
pp. 413-424
Author(s):  
Deo Brat Ojha
Keyword(s):  
Continuous Time ◽  
Efficient Solutions ◽  
Weak Duality ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Converse Duality ◽  
Multi Objective ◽  
Properly Efficient Solutions ◽  
Self Duality ◽  
Duality Relations

We introduced a symmetric dual for multi objective fractional variational programs in second order. Under invexity assumptions, we established weak, strong and converse duality as well as self duality relations .We work with properly efficient solutions in strong and converse duality theorems. The weak duality theorems involves efficient solutions .

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 Mond-Weir type second order multiobjective mixed symmetric duality with square root term under generalized univex function

2013 ◽  
Vol 4 (1) ◽  
pp. 21-33
Author(s):  
Arun Kumar Tripathy
Keyword(s):  
Second Order ◽  
Nondifferentiable Programming ◽  
Square Root ◽  
Symmetric Duality ◽  
New Class ◽  
Duality Results ◽  
Special Cases ◽  
Mild Assumption ◽  
Root Term

In this paper, a new class of second order (Φ,ρ)-univex and second order (Φ,ρ)-pseudo univex function are introduced with example. A pair Mond-Weir type second order mixed symmetric duality for multiobjective nondifferentiable programming is formulated and the duality results are established under the mild assumption of second order (∅,ρ) univexity and second order pseudo univexity. Special cases are discussed to show that this study extends some of the known results in related domain..

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 Multiobjective Fractional Symmetric Duality in Mathematical Programming with (C,Gf)-Invexity Assumptions

Axioms ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 97 ◽  
Author(s):  
Ramu Dubey ◽  
Lakshmi Narayan Mishra ◽  
Clemente Cesarano
Keyword(s):  
Mathematical Programming ◽  
Generalized Convexity ◽  
Symmetric Duality ◽  
Numerical Examples ◽  
Invex Functions ◽  
New Class ◽  
Duality Results

In this paper, a new class of ( C , G f ) -invex functions introduce and give nontrivial numerical examples which justify exist such type of functions. Also, we construct generalized convexity definitions (such as, ( F , G f ) -invexity, C-convex etc.). We consider Mond–Weir type fractional symmetric dual programs and derive duality results under ( C , G f ) -invexity assumptions. Our results generalize several known results in the literature.

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 Wolfe Type Second Order Nondifferentiable Symmetric Duality in Multiobjective Programming over Cone with Generalized (K, F)-Convexity

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
A. K. Tripathy
Keyword(s):  
Multiobjective Programming ◽  
Second Order ◽  
Mixed Integer ◽  
Integer Programming Problem ◽  
Symmetric Duality ◽  
New Class ◽  
Duality Results ◽  
Pseudoconvex Function ◽  
Root Term ◽  
Mixed Integer Programming Problem

A new class of second order (K, F) pseudoconvex function is introduced with example. A pair of Wolfe type second order nondifferentiable symmetric dual programs over arbitrary cones with square root term is formulated. The duality results are established under second order (K, F) pseudoconvexity assumption. Also a Wolfe type second order minimax mixed integer programming problem is formulated and the symmetric duality results are established under second order (K, F) pseudoconvexity assumption.

Sign in / Sign up

Export Citation Format

Share Document