scholarly journals Second-order symmetric duality in multiobjective variational problems

2019 ◽  
Vol 29 (3) ◽  
pp. 295-308
Author(s):  
Geeta Sachdev ◽  
Khushboo Verma ◽  
T.R. Gulati
Keyword(s):  
Variational Problems ◽  
Second Order ◽  
Static Case ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Converse Duality ◽  
Multiobjective Variational Problems ◽  
Second Order Symmetric Duality

In this work, we introduce a pair of multiobjective second-order symmetric dual variational problems. Weak, strong, and converse duality theorems for this pair are established under the assumption of ?-bonvexity/?-pseudobonvexity. At the end, the static case of our problems has also been discussed.

scholarly journals Mixed type second-order symmetric duality under F-convexity

2012 ◽  
Vol 3 (1) ◽  
pp. 1-5 ◽  
Author(s):  
Tilak Raj GULATI ◽  
Khushboo VERMA
Keyword(s):  
Mixed Type ◽  
Second Order ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Converse Duality ◽  
Dual Problems ◽  
Second Order Symmetric Duality ◽  
Convexity Assumptions

We introduce a pair of second order mixed symmetric dual problems. Weak, strong and converse duality theorems for this pair are established under $F-$convexity assumptions.

scholarly journals Duality for a class of second order symmetric nondifferentiable fractional variational problems

2020 ◽  
Vol 30 (2) ◽  
pp. 121-136
Author(s):  
Ashish Prasad ◽  
Anant Singh ◽  
Sony Khatri
Keyword(s):  
Variational Problems ◽  
Second Order ◽  
Static Case ◽  
Time Dependency ◽  
Duality Theorems ◽  
Support Functions ◽  
Converse Duality ◽  
Cone Constraints ◽  
Fractional Variational Problems ◽  
Convexity Assumptions

The present work frames a pair of symmetric dual problems for second order nondifferentiable fractional variational problems over cone constraints with the help of support functions. Weak, strong and converse duality theorems are derived under second order F-convexity assumptions. By removing time dependency, static case of the problem is obtained. Suitable numerical example is constructed.

scholarly journals Second order symmetric duality in fractional variational problems over cone constraints

2018 ◽  
Vol 28 (1) ◽  
pp. 39-57
Author(s):  
Anurag Jayswal ◽  
Shalini Jha
Keyword(s):  
Duality Theorem ◽  
Variational Problems ◽  
Second Order ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Self Duality ◽  
Cone Constraints ◽  
Fractional Variational Problems ◽  
Second Order Symmetric Duality ◽  
Convexity Assumptions

In the present paper, we introduce a pair of second order fractional symmetric variational programs over cone constraints and derive weak, strong, and converse duality theorems under second order F-convexity assumptions. Moreover, self duality theorem is also discussed. Our results give natural unification and extension of some previously known results in the literature.

Second-Order Symmetric Duality in Variational Control Problems Over Cone Constraints

2018 ◽  
Vol 35 (04) ◽  
pp. 1850028
Author(s):  
Anurag Jayswal ◽  
Shalini Jha ◽  
Ashish Kumar Prasad ◽  
Izhar Ahmad
Keyword(s):  
Duality Theorem ◽  
Second Order ◽  
Control Problems ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Control Programs ◽  
Convexity Assumption ◽  
Self Duality ◽  
Cone Constraints ◽  
Second Order Symmetric Duality

In the present paper, we introduce a pair of multiobjective second-order symmetric variational control programs over cone constraints and derive weak, strong and converse duality theorems under second-order [Formula: see text]-convexity assumption. Moreover, self-duality theorem is also discussed. Our results extend some of the known results in literature.

scholarly journals On second- order symmetric duality for a class of multiobjective fractional programming problem

2012 ◽  
Vol 43 (2) ◽  
pp. 267-279 ◽  
Author(s):  
Deo Brat Ojha
Keyword(s):  
Fractional Programming ◽  
Strong Duality ◽  
Second Order ◽  
Multiobjective Fractional Programming ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Multiobjective Fractional Programming Problem ◽  
Special Cases ◽  
Second Order Symmetric Duality ◽  
Dual Models

This article is concerned with a pair of second-order symmetric duals in the context of non-differentiable multiobjective fractional programming problems. We establish the weak and strong duality theorems for the new pair of dual models. Discussion on some special cases shows that results in this paper extend previous work in this area.

scholarly journals Duality for multiobjective variational problems under second-order (Ф,ρ)-invexity

Filomat ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 605-615
Author(s):  
Vivek Singh ◽  
I. Ahmad ◽  
S.K. Gupta ◽  
S. Al-Homidan
Keyword(s):  
Variational Problem ◽  
Dual Problem ◽  
Variational Problems ◽  
Efficient Solutions ◽  
Second Order ◽  
Duality Theorems ◽  
Primal Problem ◽  
Duality Relations ◽  
Multiobjective Variational Problems ◽  
Invex Function

The purpose of this article is to introduce the concept of second order (?,?)-invex function for continuous case and apply it to discuss the duality relations for a class of multiobjective variational problem. Weak, strong and strict duality theorems are obtained in order to relate efficient solutions of the primal problem and its second order Mond-Weir type multiobjective variational dual problem using aforesaid assumption. A non-trivial example is also exemplified to show the presence of the proposed class of a function.

NONDIFFERENTIABLE SECOND-ORDER SYMMETRIC DUALITY

2005 ◽  
Vol 22 (01) ◽  
pp. 19-31 ◽  
Author(s):  
I. AHMAD ◽  
Z. HUSAIN
Keyword(s):  
Strong Duality ◽  
Second Order ◽  
Mixed Integer ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Dual Problems ◽  
Self Duality ◽  
Second Order Symmetric Duality ◽  
Primal And Dual Problems ◽  
Primal And Dual

A pair of Mond–Weir type nondifferentiable second-order symmetric primal and dual problems in mathematical programming is formulated. Weak duality, strong duality, and converse duality theorems are established under η-pseudobonvexity assumptions. Symmetric minimax mixed integer primal and dual problems are also investigated. Moreover, the self duality theorem is also discussed.

scholarly journals Generalized Second-Order Mixed Symmetric Duality in Nondifferentiable Mathematical Programming

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Izhar Ahmad ◽  
S. K. Gupta ◽  
N. Kailey
Keyword(s):  
Mathematical Programming ◽  
Second Order ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Converse Duality ◽  
Nondifferentiable Functions

This paper is concerned with a pair of second-order mixed symmetric dual programs involving nondifferentiable functions. Weak, strong, and converse duality theorems are proved for aforementioned pair using the notion of second-orderF-convexity/pseudoconvexity assumptions.

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