scholarly journals Second-Order Parametric Free Dualities for Complex Minimax Fractional Programming

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 67
Author(s):  
Tone-Yau Huang
Keyword(s):  
Programming Problem ◽  
Fractional Programming ◽  
Second Order ◽  
Duality Theorems ◽  
Complex Spaces ◽  
Minimax Fractional Programming ◽  
Duality Model ◽  
Wolfe Type Dual ◽  
Complex Minimax Fractional Programming ◽  
Dual Models

In this paper, we will consider a minimax fractional programming in complex spaces. Since a duality model in a programming problem plays an important role, we will establish the second-order Mond–Weir type and Wolfe type dual models, and derive the weak, strong, and strictly converse duality theorems.

scholarly journals On Second-Order Duality for Minimax Fractional Programming Problems with Generalized Convexity

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Izhar Ahmad
Keyword(s):  
Programming Problem ◽  
Fractional Programming ◽  
Generalized Convexity ◽  
Second Order ◽  
Fractional Programming Problem ◽  
Second Order Duality ◽  
Minimax Fractional Programming ◽  
Dual Models

We focus our study on a discussion of duality relationships of a minimax fractional programming problem with its two types of second-order dual models under the second-order generalized convexity type assumptions. Results obtained in this paper naturally unify and extend some previously known results on minimax fractional programming in the literature.

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.

scholarly journals Minimax fractional programming involving generalised invex functions

2003 ◽  
Vol 44 (3) ◽  
pp. 339-354 ◽  
Author(s):  
H. C. Lai ◽  
J. C. Liu
Keyword(s):  
Fractional Programming ◽  
Sufficient Optimality Conditions ◽  
Duality Theorems ◽  
Existence Of A Solution ◽  
Invex Functions ◽  
Minimax Fractional Programming ◽  
Convexity Assumptions ◽  
Wolfe Type Dual ◽  
Dual Models ◽  
Variational Type

AbstractThe convexity assumptions for a minimax fractional programming problem of variational type are relaxed to those of a generalised invexity situation. Sufficient optimality conditions are established under some specific assumptions. Employing the existence of a solution for the minimax variational fractional problem, three dual models, the Wolfe type dual, the Mond-Weir type dual and a one parameter dual type, are constructed. Several duality theorems concerning weak, strong and strict converse duality under the framework of invexity are proved.

scholarly journals On second- order symmetric duality for a class of multiobjective fractional programming problem

2012 ◽  
Vol 43 (2) ◽  
pp. 267-279 ◽  
Author(s):  
Deo Brat Ojha
Keyword(s):  
Fractional Programming ◽  
Strong Duality ◽  
Second Order ◽  
Multiobjective Fractional Programming ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Multiobjective Fractional Programming Problem ◽  
Special Cases ◽  
Second Order Symmetric Duality ◽  
Dual Models

This article is concerned with a pair of second-order symmetric duals in the context of non-differentiable multiobjective fractional programming problems. We establish the weak and strong duality theorems for the new pair of dual models. Discussion on some special cases shows that results in this paper extend previous work in this area.

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 Optimality and Duality for Nondifferentiable Minimax Fractional Programming with Generalized Convexity

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Anurag Jayswal
Keyword(s):  
Fractional Programming ◽  
Generalized Convexity ◽  
Optimality Criteria ◽  
Sufficient Optimality Conditions ◽  
View Point ◽  
Generalized Convex Functions ◽  
Duality Results ◽  
Minimax Fractional Programming ◽  
Optimality And Duality ◽  
Dual Models

We establish several sufficient optimality conditions for a class of nondifferentiable minimax fractional programming problems from a view point of generalized convexity. Subsequently, these optimality criteria are utilized as a basis for constructing dual models, and certain duality results have been derived in the framework of generalized convex functions. Our results extend and unify some known results on minimax fractional programming problems.

scholarly journals On second order duality for nondifferentiable minimax fractional programming problems involving type-I functions

2014 ◽  
Vol 55 ◽  
pp. 479 ◽  
Author(s):  
S. K. Gupta ◽  
D. Dangar ◽  
I. Ahamd
Keyword(s):  
Fractional Programming ◽  
Second Order ◽  
Type I ◽  
Second Order Duality ◽  
Minimax Fractional Programming
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