Finding proper efficient solutions in fuzzy multiobjective fractional programming

2006 ◽  
Vol 9 (2) ◽  
pp. 485-496 ◽  
Author(s):  
Omar M. Saad
Keyword(s):  
Fractional Programming ◽  
Efficient Solutions ◽  
Multiobjective Fractional Programming ◽  
Proper Efficient Solutions

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.

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.

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

scholarly journals Symmetric dual multiobjective fractional programming

1991 ◽  
Vol 50 (1) ◽  
pp. 67-74 ◽  
Author(s):  
T. Weir
Keyword(s):  
Fractional Programming ◽  
Multiobjective Fractional Programming ◽  
Duality Theorems

AbstractA pair of symmetric dual multiobjective fractional programming problems is formulated and appropriate duality theorems are established.

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