scholarly journals Nonsmooth Multiobjective Fractional Programming with Local Lipschitz ExponentialB-p,r-Invexity

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Shun-Chin Ho
Keyword(s):  
Optimality Conditions ◽  
Fractional Programming ◽  
Strong Duality ◽  
Sufficient Optimality Conditions ◽  
Multiobjective Fractional Programming ◽  
Nonconvex Functions ◽  
Invex Functions ◽  
Multiobjective Fractional Programming Problem ◽  
Duality Model ◽  
Duality Problem

We study nonsmooth multiobjective fractional programming problem containing local Lipschitz exponentialB-p,r-invex functions with respect toηandb. We introduce a new concept of nonconvex functions, called exponentialB-p,r-invex functions. Base on the generalized invex functions, we establish sufficient optimality conditions for a feasible point to be an efficient solution. Furthermore, employing optimality conditions to perform Mond-Weir type duality model and prove the duality theorems including weak duality, strong duality, and strict converse duality theorem under exponentialB-p,r-invexity assumptions. Consequently, the optimal values of the primal problem and the Mond-Weir type duality problem have no duality gap under the framework of exponentialB-p,r-invexity.

scholarly journals Efficiency and duality in nonsmooth multiobjective fractional programming involving η-pseudolinear functions

2012 ◽  
Vol 22 (1) ◽  
pp. 3-18 ◽  
Author(s):  
S.K. Mishra ◽  
B.B. Upadhyay
Keyword(s):  
Fractional Programming ◽  
Dual Problem ◽  
Feasible Solution ◽  
Strong Duality ◽  
Sufficient Optimality Conditions ◽  
Boundedness Condition ◽  
Multiobjective Fractional Programming ◽  
Duality Results ◽  
Multiobjective Fractional Programming Problem ◽  
Necessary And Sufficient

In this paper, we shall establish necessary and sufficient optimality conditions for a feasible solution to be efficient for a nonsmooth multiobjective fractional programming problem involving ?-pseudolinear functions. Furthermore, we shall show equivalence between efficiency and proper efficiency under certain boundedness condition. We have also obtained weak and strong duality results for corresponding Mond-Weir subgradient type dual problem. These results extend some earlier results on efficiency and duality to multiobjective fractional programming problems involving ?-pseudolinear and pseudolinear functions.

scholarly journals Sufficient optimality conditions for semi-infinite multiobjective fractional programming under (Ф,ρ)-V-invexity and generalized (Ф,ρ)-V-invexity

Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3649-3665 ◽  
Author(s):  
Tadeusz Antczak
Keyword(s):  
Optimality Conditions ◽  
Fractional Programming ◽  
Generalized Convexity ◽  
Optimization Problems ◽  
Fundamental Property ◽  
Efficient Solutions ◽  
Sufficient Optimality Conditions ◽  
Multiobjective Fractional Programming ◽  
New Class ◽  
Multiobjective Programming Problems

A new class of nonconvex smooth semi-infinite multiobjective fractional programming problems with both inequality and equality constraints is considered. We formulate and establish several parametric sufficient optimality conditions for efficient solutions in such nonconvex vector optimization problems under (?,?)-V-invexity and/or generalized (?,?)-V-invexity hypotheses. With the reference to the said functions, we extend some results of efficiency for a larger class of nonconvex smooth semi-infinite multiobjective programming problems in comparison to those ones previously established in the literature under other generalized convexity notions. Namely, we prove the sufficient optimality conditions for such nonconvex semi-infinite multiobjective fractional programming problems in which not all functions constituting them have the fundamental property of convexity, invexity and most generalized convexity notions.

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 Higher order duality in multiobjective fractional programming problem with generalized convexity

2017 ◽  
Vol 27 (2) ◽  
pp. 249-264
Author(s):  
P Pankaj ◽  
Bhuwan Joshi
Keyword(s):  
Programming Problem ◽  
Fractional Programming ◽  
Generalized Convexity ◽  
Higher Order ◽  
Multiobjective Fractional Programming ◽  
Fractional Programming Problem ◽  
Invex Functions ◽  
Multiobjective Fractional Programming Problem ◽  
Invex Function ◽  
Higher Order Duality

We have introduced higher order generalized hybrid B -(b,?,?,??,?r)-invex function. Then, we have estabilished higher order weak, strong and strict converse duality theorems for a multiobjective fractional programming problem with support function in the numerator of the objective function involving higher order generalized hybrid B -(b,?,?,??,?r)-invex functions. Our results extend and unify several results from the literature.

scholarly journals Sufficient Conditions and Duality Theorems for Nondifferentiable Minimax Fractional Programming

2011 ◽  
Vol 2011 ◽  
pp. 1-22
Author(s):  
Shun-Chin Ho
Keyword(s):  
Optimality Conditions ◽  
Fractional Programming ◽  
Sufficient Conditions ◽  
Sufficient Optimality Conditions ◽  
Duality Theorems ◽  
Invex Functions ◽  
Duality Results ◽  
Wolfe Duality ◽  
Minimax Fractional Programming

We consider nondifferentiable minimax fractional programming problems involving B-(p, r)-invex functions with respect to η and b. Sufficient optimality conditions and duality results for a class of nondifferentiable minimax fractional programming problems are obtained undr B-(p, r)-invexity assumption on objective and constraint functions. Parametric duality, Mond-Weir duality, and Wolfe duality problems may be formulated, and duality results are derived under B-(p, r)-invex functions.

scholarly journals Optimality and Duality for Multiobjective Fractional Programming Involving Nonsmooth Generalized(ℱ,b,ϕ,ρ,θ)-Univex Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Jen-Chwan Liu ◽  
Chun-Yu Liu
Keyword(s):  
Optimality Conditions ◽  
Fractional Programming ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Dual Model ◽  
Multiobjective Fractional Programming ◽  
Duality Results ◽  
Optimality And Duality ◽  
Necessary And Sufficient

We establish properly efficient necessary and sufficient optimality conditions for multiobjective fractional programming involving nonsmooth generalized(ℱ,b,ϕ,ρ,θ)-univex functions. Utilizing the necessary optimality conditions, we formulate the parametric dual model and establish some duality results in the framework of generalized(ℱ,b,ϕ,ρ,θ)-univex functions.

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