Optimality conditions and duality for nondifferentiable multiobjective fractional programming with generalized convexity

2007 ◽  
Vol 154 (1) ◽  
pp. 133-147 ◽  
Author(s):  
Altannar Chinchuluun ◽  
Dehui Yuan ◽  
Panos M. Pardalos
Keyword(s):  
Optimality Conditions ◽  
Fractional Programming ◽  
Generalized Convexity ◽  
Multiobjective Fractional Programming

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 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 Duality for multiobjective fractional programming problems involving d -type-I n-set functions

2009 ◽  
Vol 19 (1) ◽  
pp. 63-73
Author(s):  
I.M. Stancu-Minasian ◽  
Gheorghe Dogaru ◽  
Mădălina Stancu
Keyword(s):  
Programming Problem ◽  
Fractional Programming ◽  
Generalized Convexity ◽  
Type I ◽  
Multiobjective Fractional Programming ◽  
Fractional Programming Problem ◽  
Duality Results ◽  
Set Functions ◽  
Convexity Assumptions ◽  
Nonlinear Fractional Programming

We establish duality results under generalized convexity assumptions for a multiobjective nonlinear fractional programming problem involving d -type-I n -set functions. Our results generalize the results obtained by Preda and Stancu-Minasian [24], [25].

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