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

Non-differentiable higher-order fractional programming problem and their duality results under cone-invex functions

2021 ◽  
Author(s):  
Rajesh Kumar Tripathi ◽  
Arvind Kumar ◽  
Ramu Dubey ◽  
Awanish Kumar Tiwari ◽  
Jasvendra Tyagi ◽  
...  
Keyword(s):  
Programming Problem ◽  
Fractional Programming ◽  
Higher Order ◽  
Fractional Programming Problem ◽  
Invex Functions ◽  
Duality Results

scholarly journals Duality for Unified Higher-Order Minimax Fractional Programming with Support Function under Type-I Assumptions

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1034 ◽  
Author(s):  
Ramu Dubey ◽  
Vishnu Narayan Mishra ◽  
and Rifaqat Ali
Keyword(s):  
Programming Problem ◽  
Fractional Programming ◽  
Support Function ◽  
Final Section ◽  
Higher Order ◽  
Type I ◽  
Dual Model ◽  
Duality Theorems ◽  
Fractional Programming Problem ◽  
Minimax Fractional Programming

This article is devoted to discussing the nondifferentiable minimax fractional programming problem with type-I functions. We focus our study on a nondifferentiable minimax fractional programming problem and formulate a higher-order dual model. Next, we establish weak, strong, and strict converse duality theorems under generalized higher-order strictly pseudo ( V , α , ρ , d ) -type-I functions. In the final section, we turn our focus to study a nondifferentiable unified minimax fractional programming problem and the results obtained in this paper naturally unify. Further, we extend some previously known results on nondifferentiable minimax fractional programming in the literature.

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 Higher-order symmetric duality in nondifferentiable multiobjective fractional programming problem over cone contraints

2020 ◽  
Vol 8 (1) ◽  
pp. 187-205 ◽  
Author(s):  
Ramu Dubey ◽  
Deepmala ◽  
Vishnu Narayan Mishra
Keyword(s):  
Programming Problem ◽  
Fractional Programming ◽  
Higher Order ◽  
Multiobjective Fractional Programming ◽  
Symmetric Duality ◽  
Numerical Examples ◽  
Fractional Programming Problem ◽  
Multiobjective Fractional Programming Problem ◽  
Duality Relations ◽  
Definition Of

In this paper, we introduce the definition of higher-order K-(C, α, ρ, d)-convexity/pseudoconvexity over cone and discuss a nontrivial numerical examples for existing such type of functions. The purpose of the paper is to study higher order fractional symmetric duality over arbitrary cones for nondifferentiable Mond-Weir type programs under higher- order K-(C, α, ρ, d)-convexity/pseudoconvexity assumptions. Next, we prove appropriate duality relations under aforesaid assumptions.

scholarly journals Nondifferentiable generalized minimax fractional programming under (Ф,ρ)-invexity

2021 ◽  
pp. 18-18
Author(s):  
B.B. Upadhyay ◽  
T. Antczak ◽  
S.K. Mishra ◽  
K. Shukla
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Fractional Programming ◽  
Sufficient Optimality Conditions ◽  
Duality Theorems ◽  
Dual Problems ◽  
Fractional Programming Problem ◽  
Minimax Fractional Programming ◽  
Dual Models

In this paper, a class of nonconvex nondifferentiable generalized minimax fractional programming problems is considered. Sufficient optimality conditions for the considered nondifferentiable generalized minimax fractional programming problem are established under the concept of (?,?)-invexity. Further, two types of dual models are formulated and various duality theorems relating to the primal minimax fractional programming problem and dual problems are established. The results established in the paper generalize and extend several known results in the literature to a wider class of nondifferentiable minimax fractional programming problems. To the best of our knowledge, these results have not been established till now.

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