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 Optimality and duality for a class of nondifferentiable minimax fractional programming problems

2009 ◽  
Vol 19 (1) ◽  
pp. 49-61
Author(s):  
Antoan Bătătorescu ◽  
Miruna Beldiman ◽  
Iulian Antonescu ◽  
Roxana Ciumara
Keyword(s):  
Optimality Conditions ◽  
Fractional Programming ◽  
Dual Problem ◽  
Sufficient Optimality Conditions ◽  
Square Root ◽  
Duality Results ◽  
Minimax Fractional Programming ◽  
Optimality And Duality ◽  
Necessary And Sufficient

Necessary and sufficient optimality conditions are established for a class of nondifferentiable minimax fractional programming problems with square root terms. Subsequently, we apply the optimality conditions to formulate a parametric dual problem and we prove some duality results.

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 Multiobjective Fractional Programming Involving Generalized Semilocally V-Type I-Preinvex and Related Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Hachem Slimani ◽  
Shashi Kant Mishra
Keyword(s):  
Fractional Programming ◽  
Inequality Constraints ◽  
Strong Duality ◽  
Multiple Objective ◽  
Type I ◽  
Multiobjective Fractional Programming ◽  
Duality Results ◽  
Preinvex Functions ◽  
Necessary And Sufficient ◽  
Efficiency Conditions

We study a nonlinear multiple objective fractional programming with inequality constraints where each component of functions occurring in the problem is considered semidifferentiable along its own direction instead of the same direction. New Fritz John type necessary and Karush-Kuhn-Tucker type necessary and sufficient efficiency conditions are obtained for a feasible point to be weakly efficient or efficient. Furthermore, a general Mond-Weir dual is formulated and weak and strong duality results are proved using concepts of generalized semilocally V-type I-preinvex functions. This contribution extends earlier results of Preda (2003), Mishra et al. (2005), Niculescu (2007), and Mishra and Rautela (2009), and generalizes results obtained in the literature on this topic.

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.

scholarly journals Second Order Duality in Multiobjective Fractional Programming with Square Root Term under Generalized Univex Function

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Arun Kumar Tripathy
Keyword(s):  
Fractional Programming ◽  
Sufficient Conditions ◽  
Positive Semidefinite ◽  
Second Order ◽  
Square Root ◽  
Multiobjective Fractional Programming ◽  
Multiobjective Fractional Programming Problem ◽  
Second Order Duality ◽  
Root Term ◽  
Necessary And Sufficient

Three approaches of second order mixed type duality are introduced for a nondifferentiable multiobjective fractional programming problem in which the numerator and denominator of objective function contain square root of positive semidefinite quadratic form. Also, the necessary and sufficient conditions of efficient solution for fractional programming are established and a parameterization technique is used to establish duality results under generalized second order ρ-univexity assumption.

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.

APPROXIMATE EFFICIENCY FOR n-SET MULTIOBJECTIVE FRACTIONAL PROGRAMMING

2004 ◽  
Vol 21 (02) ◽  
pp. 197-206 ◽  
Author(s):  
NARENDER KUMAR ◽  
R. K. BUDHRAJA ◽  
APARNA MEHRA
Keyword(s):  
Fractional Programming ◽  
Sufficient Conditions ◽  
Approximate Solutions ◽  
Efficient Solutions ◽  
Parametric Approach ◽  
Multiobjective Fractional Programming ◽  
Set Functions ◽  
New Concepts ◽  
Multiobjective Fractional Programming Problem ◽  
Necessary And Sufficient

In this paper, we introduce new concepts of ε-weak efficient solutions and ε-efficient solutions for a nonconvex multiobjective fractional programming problem involving n-set functions. Using an ε-parametric approach and a new theorem of alternative for nonconvex n-set functions, some necessary and sufficient conditions for ε-approximate solutions are derived

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