scholarly journals HIGHER ORDER DUALITY FOR A NEW CLASS OF NONCONVEX SEMI-INFINITE MULTIOBJECTIVE FRACTIONAL PROGRAMMING WITH SUPPORT FUNCTIONS

2020 ◽  
Vol 10 (6) ◽  
pp. 2806-2825
Author(s):  
Tadeusz Antczak ◽  
◽  
Kalpana Shukla ◽  
Keyword(s):  
Fractional Programming ◽  
Higher Order ◽  
Multiobjective Fractional Programming ◽  
Support Functions ◽  
New Class ◽  
Higher Order Duality

Higher order duality for cone vector optimization problems

2018 ◽  
Vol 13 (01) ◽  
pp. 2050020
Author(s):  
Vivek Singh ◽  
Anurag Jayswal ◽  
S. Al-Homidan ◽  
I. Ahmad
Keyword(s):  
Vector Optimization ◽  
Optimization Problems ◽  
Strong Duality ◽  
Vector Optimization Problem ◽  
Higher Order ◽  
Support Functions ◽  
Invex Functions ◽  
New Class ◽  
Duality Results ◽  
Higher Order Duality

In this paper, we present a new class of higher order [Formula: see text]-[Formula: see text]-invex functions over cones. Further, we formulate two types of higher order dual models for a vector optimization problem over cones containing support functions in objectives as well as in constraints and establish several duality results, viz., weak and strong duality results.

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 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.

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