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.

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 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 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 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.

A NOTE ON MOND-WEIR TYPE SECOND-ORDER SYMMETRIC DUALITY

2007 ◽  
Vol 24 (05) ◽  
pp. 737-740 ◽  
Author(s):  
T. R. GULATI ◽  
S. K. GUPTA
Keyword(s):  
Duality Theorem ◽  
Strong Duality ◽  
Second Order ◽  
Symmetric Duality ◽  
Dual Problems ◽  
Second Order Symmetric Duality

In this paper, we establish a strong duality theorem for a pair of Mond–Weir type second-order nondifferentiable symmetric dual problems. This removes certain inconsistencies in some of the earlier results.

scholarly journals Multiobjective duality with ρ−(η,θ)-invexity

2005 ◽  
Vol 2005 (2) ◽  
pp. 175-180 ◽  
Author(s):  
C. Nahak ◽  
S. Nanda
Keyword(s):  
Programming Problem ◽  
Multiobjective Programming ◽  
Efficient Solutions ◽  
Duality Theorems ◽  
Converse Duality ◽  
Dual Problems ◽  
Properly Efficient Solutions ◽  
Multiobjective Programming Problem ◽  
Primal And Dual Problems ◽  
Primal And Dual

Under ρ−(η,θ)-invexity assumptions on the functions involved, weak, strong, and converse duality theorems are proved to relate properly efficient solutions of the primal and dual problems for a multiobjective programming problem.

On the multiobjective control problem

2018 ◽  
Vol 24 (2) ◽  
pp. 223-231
Author(s):  
Promila Kumar ◽  
Bharti Sharma
Keyword(s):  
Control Problem ◽  
Strong Duality ◽  
Efficient Solutions ◽  
Higher Order ◽  
Sufficient Optimality Conditions ◽  
Duality Theorems ◽  
Multiobjective Control ◽  
Primal And Dual Problems ◽  
Primal And Dual

Abstract In this paper, sufficient optimality conditions are established for the multiobjective control problem using efficiency of higher order as a criterion for optimality. The ρ-type 1 invex functionals (taken in pair) of higher order are proposed for the continuous case. Existence of such functionals is confirmed by a number of examples. It is shown with the help of an example that this class is more general than the existing class of functionals. Weak and strong duality theorems are also derived for a mixed dual in order to relate efficient solutions of higher order for primal and dual problems.

Wolfe-type second-order fractional symmetric duality

2014 ◽  
Vol 20 (2) ◽  
Author(s):  
Anurag Jayswal ◽  
Ioan M. Stancu-Minasian ◽  
Ashish K. Prasad
Keyword(s):  
Second Order ◽  
Mixed Integer ◽  
Symmetric Duality ◽  
Duality Results ◽  
Self Duality ◽  
Fractional Programs

AbstractIn the present paper, we examine duality results for Wolfe-type second-order fractional symmetric dual programs. These duality results are then used to investigate minimax mixed integer symmetric dual fractional programs. We also discuss self-duality results at the end.

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.

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