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 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.

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.

scholarly journals Nondifferentiable higher order symmetric duality under invexity/generalized invexity

Filomat ◽  
2014 ◽  
Vol 28 (8) ◽  
pp. 1661-1674 ◽  
Author(s):  
T.R. Gulati ◽  
Khushboo Verma
Keyword(s):  
Higher Order ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Converse Duality ◽  
Generalized Invexity ◽  
Self Duality ◽  
Special Cases ◽  
Dual Models

In this paper, we introduce a pair of nondifferentiable higher-order symmetric dual models. Weak, strong and converse duality theorems for this pair are established under the assumption of higher order invexity/generalized invexity. Self duality has been discussed assuming the function involved to be skew-symmetric. Several known results are obtained as special cases.

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 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 Optimality and duality for complex multi-objective programming

2022 ◽  
Vol 12 (1) ◽  
pp. 121
Author(s):  
Tone-Yau Huang ◽  
Tamaki Tanaka
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Efficient Solutions ◽  
Dual Model ◽  
Duality Theorems ◽  
Multi Objective ◽  
Multi Objective Programming ◽  
Optimality And Duality ◽  
Objective Programming

<p style='text-indent:20px;'>We consider a complex multi-objective programming problem (CMP). In order to establish the optimality conditions of problem (CMP), we introduce several properties of optimal efficient solutions and scalarization techniques. Furthermore, a certain parametric dual model is discussed, and their duality theorems are proved.</p>

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.

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.

Sign in / Sign up

Export Citation Format

Share Document