Parametric duality models for discrete minmax fractional programming problems containing generalized (θ,η,ρ)-V- invex functions and arbitrary norms

2007 ◽  
Vol 24 (1-2) ◽  
pp. 105-126 ◽  
Author(s):  
G. J. Zalmai
Keyword(s):  
Fractional Programming ◽  
Invex Functions ◽  
Arbitrary Norms

Higher-order fractional programming problem and their duality theorems in vector optimization with cone-η − invex functions

2021 ◽  
Author(s):  
Tarun Kumar Gupta ◽  
Rajesh Kumar Tripathi ◽  
Chetan Swarup ◽  
Kuldeep Singh ◽  
Ramu Dubey ◽  
...  
Keyword(s):  
Programming Problem ◽  
Vector Optimization ◽  
Fractional Programming ◽  
Higher Order ◽  
Duality Theorems ◽  
Fractional Programming Problem ◽  
Invex Functions

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 problems and the sufficient condition involving Hb – (p, r)-η- invex function

2021 ◽  
Vol 336 ◽  
pp. 08015
Author(s):  
Xiaoyan Gao ◽  
Huan Niu
Keyword(s):  
Convex Functions ◽  
Fractional Programming ◽  
Efficient Solutions ◽  
Sufficient Condition ◽  
Sufficient Optimality Condition ◽  
Multiobjective Fractional Programming ◽  
Invex Functions ◽  
Arcwise Connected ◽  
Feasible Solutions ◽  
Invex Function

On the basis of arcwise connected convex functions and (p, r) −η - invex functions, we established Hb –(p, r) –η- invex functions. Based on the generalized invex assumption of new functions, the solutions of a class of multiobjective fractional programming problems are studied, and the sufficient optimality condition for the feasible solutions of multiobjective fractional programming problems to be efficient solutions are established and proved.

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