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.

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 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 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.

scholarly journals Mixed Type Nondifferentiable Higher-Order Symmetric Duality over Cones

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 274 ◽  
Author(s):  
Izhar Ahmad ◽  
Khushboo Verma ◽  
Suliman Al-Homidan
Keyword(s):  
Mixed Type ◽  
Higher Order ◽  
Dual Model ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Converse Duality ◽  
Self Duality ◽  
Pseudoconvex Functions

A new mixed type nondifferentiable higher-order symmetric dual programs over cones is formulated. As of now, in the literature, either Wolfe-type or Mond–Weir-type nondifferentiable symmetric duals have been studied. However, we present a unified dual model and discuss weak, strong, and converse duality theorems for such programs under higher-order F - convexity/higher-order F - pseudoconvexity. Self-duality is also discussed. Our dual programs and results generalize some dual formulations and results appeared in the literature. Two non-trivial examples are given to show the uniqueness of higher-order F - convex/higher-order F - pseudoconvex functions and existence of higher-order symmetric dual programs.

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 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 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.

scholarly journals Duality for mixed second-order programs with multiple arguments

Filomat ◽  
2014 ◽  
Vol 28 (2) ◽  
pp. 397-410
Author(s):  
N. Kailey ◽  
S.K. Gupta
Keyword(s):  
Duality Theory ◽  
Major Part ◽  
Second Order ◽  
Linear Programs ◽  
Duality Theorems ◽  
Converse Duality ◽  
Dual Problems ◽  
Special Cases ◽  
Non Linear ◽  
Broad Framework

The duality theory is well-developed for non linear programs. Technically, a major part of such broad framework possibly be extended to mixed non linear programs, however this has demonstrated complicated, in minority as the duality theory does not integrate well with modern computational practice. In this paper, we constructed a new pair of second-order multiobjective mixed dual problems over arbitrary cones with multiple arguments, with an eye towards developing a more practical framework. Weak, strong and converse duality theorems are then established under K-?-bonvexity assumptions. Several known results are obtained as special cases.

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.

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